{"id":32678,"date":"2024-01-15T15:14:40","date_gmt":"2024-01-15T15:14:40","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=32678"},"modified":"2024-01-15T15:19:47","modified_gmt":"2024-01-15T15:19:47","slug":"clase-digital-10-ecuaciones-exponenciales-y-logaritmicas","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-10-ecuaciones-exponenciales-y-logaritmicas\/","title":{"rendered":"Clase digital 10. Ecuaciones exponenciales y logar\u00edtmicas"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover is-light\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"wp-block-cover__background has-background-dim-40 has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-32680\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_EcuacionesExponencialesLogaritmicas.jpg\" style=\"object-position:41% 23%\" data-object-fit=\"cover\" data-object-position=\"41% 23%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"639\" height=\"404\" class=\"wp-block-cover__image-background wp-image-32680\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_EcuacionesExponencialesLogaritmicas.jpg\" style=\"object-position:41% 23%\" data-object-fit=\"cover\" data-object-position=\"41% 23%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_EcuacionesExponencialesLogaritmicas.jpg 639w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_EcuacionesExponencialesLogaritmicas-300x190.jpg 300w\" sizes=\"auto, (max-width: 639px) 100vw, 639px\" \/><\/noscript><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-base-3-color has-text-color has-large-font-size wp-block-paragraph\"><br>Ecuaciones exponenciales y logar\u00edtmicas<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"introduccion\">Introducci\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">En 1859, un terrateniente australiano llamado Thomas Austin liber\u00f3 24 conejos en la naturaleza para su caza. Debido a que Australia ten\u00eda pocos depredadores y abundante comida, la poblaci\u00f3n de conejos se dispar\u00f3. En menos de diez a\u00f1os, la poblaci\u00f3n de conejos se contaba por millones.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El crecimiento demogr\u00e1fico descontrolado, como en el caso de los conejos silvestres de Australia, puede modelarse con funciones exponenciales. Las ecuaciones resultantes de esas funciones exponenciales pueden resolverse para analizar y hacer predicciones sobre el crecimiento exponencial.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A una ecuaci\u00f3n cuya variable es un exponente se le llama ecuaci\u00f3n exponencial, y a una ecuaci\u00f3n que contiene expresiones logar\u00edtmicas de por lo menos una variable se le llama ecuaci\u00f3n logar\u00edtmica.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Desarrollo del tema <\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Ecuaci\u00f3n exponencial<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">En la funci\u00f3n exponencial:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_1.png\" alt=\"\" class=\"wp-image-32921\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"114\" height=\"45\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_1.png\" alt=\"\" class=\"wp-image-32921\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">identifica que la variable \u00ab<em>x<\/em>\u00bb es el exponente, y que cuando se desconoce su valor se origina una ecuaci\u00f3n exponencial. A continuaci\u00f3n, analiza y asimila los ejemplos que muestran el procedimiento de resolver ecuaciones exponenciales. Por el momento, s\u00f3lo se contemplan ecuaciones exponenciales cuya soluci\u00f3n es por medio de potencias de igual base.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Utiliza potencias de igual base en la soluci\u00f3n de las siguientes ecuaciones exponenciales:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Primer ejemplo:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_2.png\" alt=\"\" class=\"wp-image-32922\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"195\" height=\"41\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_2.png\" alt=\"\" class=\"wp-image-32922\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Expresa 100 y 1000 en potencias de 10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Concluye que 100 = (10)<sup>2<\/sup> y 1000 = (10)<sup>3<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sustituye 100 = (10)<sup>2<\/sup> y 1000 = (10)<sup>3<\/sup> en la ecuaci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_5.png\" alt=\"\" class=\"wp-image-32925\" \/><noscript><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_5.png\" alt=\"\" class=\"wp-image-32925\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"214\" height=\"47\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_5.png\" alt=\"\" class=\"wp-image-32925\" \/><\/noscript><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Aplica propiedades de exponentes:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_5.png\" alt=\"\" class=\"wp-image-32925\" \/><noscript><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_5.png\" alt=\"\" class=\"wp-image-32925\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"214\" height=\"47\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_5.png\" alt=\"\" class=\"wp-image-32925\" \/><\/noscript><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Como la ecuaci\u00f3n tienen potencias de igual base, los exponentes deben ser iguales.<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Por lo tanto: 6x &#8211; 2 = 3x + 3<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Aplica la propiedad aditiva: 6x &#8211; 3x = 3 + 2<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Reduce la propiedad aditiva: 6x &#8211; 3x = 3 + 2 <\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Reduce t\u00e9rminos semejantes: 3x = 5<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Concluye que la soluci\u00f3n es: x = 5\/3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Segundo ejemplo:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_6.png\" alt=\"\" class=\"wp-image-32926\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"201\" height=\"44\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_6.png\" alt=\"\" class=\"wp-image-32926\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Expresa 4, 8 y 0.5 en potencias de 2, esto es 4 = (2)<sup>2<\/sup>, 8 = (2)<sup>3<\/sup> y 0.5 = (2)<sup>-1<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sustituye 4 = (2)<sup>2<\/sup>, 8 = (2)<sup>3<\/sup> y 0.5 = (2)<sup>-1<\/sup> en la ecuaci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_8.png\" alt=\"\" class=\"wp-image-32928\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"259\" height=\"47\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_8.png\" alt=\"\" class=\"wp-image-32928\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Aplica propiedades de exponentes:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_7.png\" alt=\"\" class=\"wp-image-32927\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"205\" height=\"44\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_7.png\" alt=\"\" class=\"wp-image-32927\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Aplica el producto de potencias de igual base:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_9.png\" alt=\"\" class=\"wp-image-32929\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"129\" height=\"43\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_9.png\" alt=\"\" class=\"wp-image-32929\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Como la ecuaci\u00f3n tienen potencias de igual base, los exponentes deben ser iguales.<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Por lo tanto: 5x = -x + 1<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Aplica la propiedad aditiva: 5x + x = 1<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Reduce t\u00e9rminos semejantes: 6x = 1<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Concluye que la soluci\u00f3n es: x = 1\/6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tercer ejemplo:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_10.png\" alt=\"\" class=\"wp-image-32930\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"204\" height=\"42\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_10.png\" alt=\"\" class=\"wp-image-32930\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Utiliza factorizaci\u00f3n de un trinomio de la forma:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_11.png\" alt=\"\" class=\"wp-image-32931\" \/><noscript><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_11.png\" alt=\"\" class=\"wp-image-32931\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"171\" height=\"40\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_11.png\" alt=\"\" class=\"wp-image-32931\" \/><\/noscript><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Factorizaci\u00f3n de: 10<sup>2x<\/sup> = (10<sup>x<\/sup>)(10<sup>x<\/sup>)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Factorizaci\u00f3n de: -90 = (-10)(9)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Comprobaci\u00f3n que: -10<sup>x<\/sup> = (-10)(10<sup>x<\/sup>) + (9)(10<sup>x<\/sup>)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Luego la factorizaci\u00f3n de la ecuaci\u00f3n es: 10<sup>2x<\/sup> &#8211; 10<sup>x<\/sup> &#8211; 90 = (10<sup>x<\/sup> &#8211; 10)(10<sup>x<\/sup> + 9) = 0<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Iguala a cero los factores: (10<sup>x<\/sup> &#8211; 10)(10<sup>x<\/sup> + 9)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Primer factor igual a cero: 10<sup>x<\/sup> &#8211; 10 = 0<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Aplica la propiedad aditiva: 10<sup>x<\/sup> = 10<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Concluye que la soluci\u00f3n es: x = 1<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Segundo factor igual a cero: 10<sup>x<\/sup> + 9 = 0<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Aplica la propiedad aditiva: 10<sup>x<\/sup> = -9<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Concluye que no hay soluci\u00f3n porque la potencia de 10<sup>x<\/sup> es positiva.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cuarto ejemplo:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_12.png\" alt=\"\" class=\"wp-image-32932\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"223\" height=\"46\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_12.png\" alt=\"\" class=\"wp-image-32932\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Expresa 4 en potencias de 2, esto es 4 = (2)<sup>2<\/sup><\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Sustituye 4 = (2)<sup>2<\/sup> en la ecuaci\u00f3n 4<sup>x<\/sup> &#8211; 20(2)<sup>x<\/sup> + 64 = (2<sup>2<\/sup>)<sup>x<\/sup> &#8211; 20(2)<sup>2<\/sup> + 64 = 0<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Aplica propiedades de exponentes: 2<sup>2x<\/sup> &#8211; 20(2)<sup>x<\/sup> + 64 = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Utiliza factorizaci\u00f3n de un trinomio de la forma:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_11.png\" alt=\"\" class=\"wp-image-32931\" \/><noscript><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_11.png\" alt=\"\" class=\"wp-image-32931\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"171\" height=\"40\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_11.png\" alt=\"\" class=\"wp-image-32931\" \/><\/noscript><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Factorizaci\u00f3n de: 2<sup>2x<\/sup> = (2<sup>x<\/sup>)(2<sup>x<\/sup>)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Factorizaci\u00f3n de: 64 = (-16)(-4)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Comprobaci\u00f3n que: -20(2<sup>x<\/sup>) = (-16)(2<sup>x<\/sup>) + (-4)(2<sup>x<\/sup>)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Luego la factorizaci\u00f3n de la ecuaci\u00f3n es: 2<sup>2x<\/sup> &#8211; 20(2<sup>x<\/sup>) + 64 = (2<sup>x<\/sup> &#8211; 16)(2<sup>x<\/sup> &#8211; 4) = 0<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Iguala a cero los factores: (2<sup>x<\/sup> &#8211; 16)(2<sup>x<\/sup> &#8211; 4)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Primer factor igual a cero: 2<sup>x<\/sup> &#8211; 16 = 0<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Aplica la propiedad aditiva: 2<sup>x<\/sup> = 16<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Sustituye 16 = (2)<sup>4<\/sup> en la ecuaci\u00f3n: 2<sup>x<\/sup> = 2<sup>4<\/sup><\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Concluye que la soluci\u00f3n es: x = 4<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Segundo factor igual a cero: 2<sup>x<\/sup> &#8211; 4 = 0<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Aplica la propiedad aditiva: 2<sup>x<\/sup> = 4<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Sustituye 4 = (2)<sup>2<\/sup> en la ecuaci\u00f3n: 2<sup>x<\/sup> = 2<sup>2<\/sup><\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Concluye que la soluci\u00f3n es: x = 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La notaci\u00f3n de la funci\u00f3n logar\u00edtmica es<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_13.png\" alt=\"\" class=\"wp-image-32933\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"191\" height=\"47\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_13.png\" alt=\"\" class=\"wp-image-32933\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">donde<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_14.png\" alt=\"\" class=\"wp-image-32934\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"136\" height=\"44\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_14.png\" alt=\"\" class=\"wp-image-32934\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">La funci\u00f3n logar\u00edtmica se define como la funci\u00f3n inversa de la funci\u00f3n exponencial, la siguiente propiedad evidencia la relaci\u00f3n que hay entre ambas funciones:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_15.png\" alt=\"\" class=\"wp-image-32935\" \/><noscript><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_15.png\" alt=\"\" class=\"wp-image-32935\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"294\" height=\"50\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_15.png\" alt=\"\" class=\"wp-image-32935\" \/><\/noscript><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Por lo que el logaritmo se define como el exponente al que se eleva una base para obtener una potencia dada.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Los siguientes ejemplos muestran la equivalencia entre potencias y logaritmos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Utiliza la propiedad:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_15.png\" alt=\"\" class=\"wp-image-32935\" \/><noscript><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_15.png\" alt=\"\" class=\"wp-image-32935\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"294\" height=\"50\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_15.png\" alt=\"\" class=\"wp-image-32935\" \/><\/noscript><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">para que transformes las siguientes potencias en logaritmos:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_16.png\" alt=\"\" class=\"wp-image-32937\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"362\" height=\"59\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_16.png\" alt=\"\" class=\"wp-image-32937\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_16.png 362w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_16-300x49.png 300w\" sizes=\"auto, (max-width: 362px) 100vw, 362px\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_18.png\" alt=\"\" class=\"wp-image-32938\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"337\" height=\"54\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_18.png\" alt=\"\" class=\"wp-image-32938\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_18.png 337w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_18-300x48.png 300w\" sizes=\"auto, (max-width: 337px) 100vw, 337px\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_19.png\" alt=\"\" class=\"wp-image-32939\" style=\"width:373px;height:auto\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"373\" height=\"80\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_19.png\" alt=\"\" class=\"wp-image-32939\" style=\"width:373px;height:auto\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_19.png 373w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_19-300x64.png 300w\" sizes=\"auto, (max-width: 373px) 100vw, 373px\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_20.png\" alt=\"\" class=\"wp-image-32940\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"382\" height=\"82\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_20.png\" alt=\"\" class=\"wp-image-32940\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_20.png 382w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_20-300x64.png 300w\" sizes=\"auto, (max-width: 382px) 100vw, 382px\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_21.png\" alt=\"\" class=\"wp-image-32941\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"354\" height=\"73\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_21.png\" alt=\"\" class=\"wp-image-32941\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_21.png 354w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_21-300x62.png 300w\" sizes=\"auto, (max-width: 354px) 100vw, 354px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Utiliza la propiedad:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_22.png\" alt=\"\" class=\"wp-image-32942\" \/><noscript><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_22.png\" alt=\"\" class=\"wp-image-32942\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"295\" height=\"48\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_22.png\" alt=\"\" class=\"wp-image-32942\" \/><\/noscript><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">para que transformes los siguientes logaritmos en potencias:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_23.png\" alt=\"\" class=\"wp-image-32949\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"344\" height=\"52\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_23.png\" alt=\"\" class=\"wp-image-32949\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_23.png 344w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_23-300x45.png 300w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_24.png\" alt=\"\" class=\"wp-image-32950\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"348\" height=\"51\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_24.png\" alt=\"\" class=\"wp-image-32950\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_24.png 348w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_24-300x44.png 300w\" sizes=\"auto, (max-width: 348px) 100vw, 348px\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_25.png\" alt=\"\" class=\"wp-image-32951\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"370\" height=\"57\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_25.png\" alt=\"\" class=\"wp-image-32951\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_25.png 370w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_25-300x46.png 300w\" sizes=\"auto, (max-width: 370px) 100vw, 370px\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_26.png\" alt=\"\" class=\"wp-image-32952\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"469\" height=\"75\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_26.png\" alt=\"\" class=\"wp-image-32952\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_26.png 469w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_26-300x48.png 300w\" sizes=\"auto, (max-width: 469px) 100vw, 469px\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_27.png\" alt=\"\" class=\"wp-image-32953\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"375\" height=\"67\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_27.png\" alt=\"\" class=\"wp-image-32953\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_27.png 375w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_27-300x54.png 300w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Utiliza la propiedad:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_22.png\" alt=\"\" class=\"wp-image-32942\" \/><noscript><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_22.png\" alt=\"\" class=\"wp-image-32942\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"295\" height=\"48\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_22.png\" alt=\"\" class=\"wp-image-32942\" \/><\/noscript><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">para que resuelvas las siguientes ecuaciones logar\u00edtmicas:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Analiza y asimila la soluci\u00f3n de la ecuaci\u00f3n:<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_28.png\" alt=\"\" class=\"wp-image-32962\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"380\" height=\"210\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_28.png\" alt=\"\" class=\"wp-image-32962\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_28.png 380w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_28-300x166.png 300w\" sizes=\"auto, (max-width: 380px) 100vw, 380px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>Analiza y asimila la soluci\u00f3n de la ecuaci\u00f3n:<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_29.png\" alt=\"\" class=\"wp-image-32963\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"455\" height=\"340\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_29.png\" alt=\"\" class=\"wp-image-32963\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_29.png 455w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_29-300x224.png 300w\" sizes=\"auto, (max-width: 455px) 100vw, 455px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>Analiza y asimila la soluci\u00f3n de la ecuaci\u00f3n:<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_30.png\" alt=\"\" class=\"wp-image-32964\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"369\" height=\"219\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_30.png\" alt=\"\" class=\"wp-image-32964\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_30.png 369w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_30-300x178.png 300w\" sizes=\"auto, (max-width: 369px) 100vw, 369px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li>Despeja el exponente \u201cn\u201d de la ecuaci\u00f3n:<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_31.png\" alt=\"\" class=\"wp-image-32965\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"631\" height=\"212\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_31.png\" alt=\"\" class=\"wp-image-32965\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_31.png 631w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_31-300x101.png 300w\" sizes=\"auto, (max-width: 631px) 100vw, 631px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n<li>Despeja el exponente de la ecuaci\u00f3n:<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_32.png\" alt=\"\" class=\"wp-image-32966\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"589\" height=\"169\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_32.png\" alt=\"\" class=\"wp-image-32966\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_32.png 589w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_32-300x86.png 300w\" sizes=\"auto, (max-width: 589px) 100vw, 589px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">A continuaci\u00f3n, te invito a visualizar el siguiente video:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/es.khanacademy.org\/math\/algebra2\/x2ec2f6f830c9fb89:exp\/x2ec2f6f830c9fb89:exp-eq-prop\/v\/solving-exponential-equations-with-exponent-properties\" target=\"_blank\" rel=\"noreferrer noopener\">Resolver ecuaciones exponenciales mediante propiedades de exponentes<\/a>.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Logaritmo de base 10<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">El logaritmo de base 10, logaritmo com\u00fan o logaritmo de Briggs es uno de los logaritmos de mayor uso.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_33.png\" alt=\"\" class=\"wp-image-32967\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"473\" height=\"87\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_33.png\" alt=\"\" class=\"wp-image-32967\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_33.png 473w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_33-300x55.png 300w\" sizes=\"auto, (max-width: 473px) 100vw, 473px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Observa que son potencias de 10 y en el s\u00edmbolo de logaritmo no se indica la base<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Los siguientes ejemplos evidencian que:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_34.png\" alt=\"\" class=\"wp-image-32968\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"346\" height=\"47\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_34.png\" alt=\"\" class=\"wp-image-32968\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_34.png 346w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_34-300x41.png 300w\" sizes=\"auto, (max-width: 346px) 100vw, 346px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<ol class=\"wp-block-list\">\n<li>Expresa las potencias de 10 en logaritmos:<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_35.png\" alt=\"\" class=\"wp-image-32969\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"426\" height=\"127\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_35.png\" alt=\"\" class=\"wp-image-32969\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_35.png 426w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_35-300x89.png 300w\" sizes=\"auto, (max-width: 426px) 100vw, 426px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Comprueba lo anterior utilizando calculadora.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>Expresa en potencias de 10 los logaritmos:<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_36.png\" alt=\"\" class=\"wp-image-32970\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"405\" height=\"163\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_36.png\" alt=\"\" class=\"wp-image-32970\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_36.png 405w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_36-300x121.png 300w\" sizes=\"auto, (max-width: 405px) 100vw, 405px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\">Logaritmo de base e, logaritmo natural o logaritmo de N\u00e9per<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Recuerda que en la clase 11 se defini\u00f3 este n\u00famero como:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_37.png\" alt=\"\" class=\"wp-image-32972\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"727\" height=\"83\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_37.png\" alt=\"\" class=\"wp-image-32972\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_37.png 727w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_37-300x34.png 300w\" sizes=\"auto, (max-width: 727px) 100vw, 727px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">El logaritmo natural tiene por base el n\u00famero e.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_38.png\" alt=\"\" class=\"wp-image-32973\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"469\" height=\"93\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_38.png\" alt=\"\" class=\"wp-image-32973\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_38.png 469w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_38-300x59.png 300w\" sizes=\"auto, (max-width: 469px) 100vw, 469px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Observa que ahora son potencias de \u201ce\u201d y el s\u00edmbolo de logaritmo es ln<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Utiliza calculadora para que obtengas el valor de los siguientes logaritmos:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_39.png\" alt=\"\" class=\"wp-image-32974\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"177\" height=\"162\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_39.png\" alt=\"\" class=\"wp-image-32974\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Ahora, utiliza que:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_41.png\" alt=\"\" class=\"wp-image-32976\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"330\" height=\"39\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_41.png\" alt=\"\" class=\"wp-image-32976\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_41.png 330w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_41-300x35.png 300w\" sizes=\"auto, (max-width: 330px) 100vw, 330px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">para que expreses los logaritmos anteriores en potencias:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_40.png\" alt=\"\" class=\"wp-image-32975\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"398\" height=\"161\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_40.png\" alt=\"\" class=\"wp-image-32975\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_40.png 398w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_40-300x121.png 300w\" sizes=\"auto, (max-width: 398px) 100vw, 398px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Utiliza calculadora para que obtengas el valor de las siguientes potencias:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_42.png\" alt=\"\" class=\"wp-image-32978\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"167\" height=\"165\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_42.png\" alt=\"\" class=\"wp-image-32978\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Ahora, utiliza que:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_43.png\" alt=\"\" class=\"wp-image-32979\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"326\" height=\"47\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_43.png\" alt=\"\" class=\"wp-image-32979\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_43.png 326w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_43-300x43.png 300w\" sizes=\"auto, (max-width: 326px) 100vw, 326px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">para que expreses las potencias de \u201ce\u201d en logaritmos:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_44.png\" alt=\"\" class=\"wp-image-32980\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"402\" height=\"168\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_44.png\" alt=\"\" class=\"wp-image-32980\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_44.png 402w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_44-300x125.png 300w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Despeja el exponente \u201cn\u201d de la ecuaci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_45.png\" alt=\"\" class=\"wp-image-32981\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"626\" height=\"316\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_45.png\" alt=\"\" class=\"wp-image-32981\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_45.png 626w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_45-300x151.png 300w\" sizes=\"auto, (max-width: 626px) 100vw, 626px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\">Propiedades de logaritmos<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">En la soluci\u00f3n de ecuaciones exponenciales y logar\u00edtmicas es de gran utilidad conocer las siguientes propiedades de logaritmos:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>El logaritmo de un producto es la suma de los logaritmos de los factores:<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_46.png\" alt=\"\" class=\"wp-image-32983\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"271\" height=\"49\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_46.png\" alt=\"\" class=\"wp-image-32983\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>El logaritmo de una divisi\u00f3n es la diferencia de los logaritmos del dividendo y divisor:<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_47.png\" alt=\"\" class=\"wp-image-32984\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"263\" height=\"69\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_47.png\" alt=\"\" class=\"wp-image-32984\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>El logaritmo de una potencia es el exponente por el logaritmo de la base:<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_48.png\" alt=\"\" class=\"wp-image-32985\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"205\" height=\"47\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_48.png\" alt=\"\" class=\"wp-image-32985\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">A continuaci\u00f3n, se tienen varios ejemplos de ecuaciones logar\u00edtmicas y exponenciales:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Utiliza las propiedades de los logaritmos en las siguientes ecuaciones logar\u00edtmicas:<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_49.png\" alt=\"\" class=\"wp-image-32986\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"721\" height=\"195\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_49.png\" alt=\"\" class=\"wp-image-32986\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_49.png 721w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_49-300x81.png 300w\" sizes=\"auto, (max-width: 721px) 100vw, 721px\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_50.png\" alt=\"\" class=\"wp-image-32989\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"530\" height=\"264\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_50.png\" alt=\"\" class=\"wp-image-32989\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_50.png 530w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_50-300x149.png 300w\" sizes=\"auto, (max-width: 530px) 100vw, 530px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>Problema de aplicaci\u00f3n de ecuaciones exponenciales y logar\u00edtmicas:<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_51.png\" alt=\"\" class=\"wp-image-32990\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"672\" height=\"516\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_51.png\" alt=\"\" class=\"wp-image-32990\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_51.png 672w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2024\/01\/CD10_AlgebraII_BG_51-300x230.png 300w\" sizes=\"auto, (max-width: 672px) 100vw, 672px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">A continuaci\u00f3n, te invito a visualizar los siguientes videos:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/es.khanacademy.org\/math\/algebra2\/x2ec2f6f830c9fb89:logs\/x2ec2f6f830c9fb89:exp-eq-log\/v\/exponential-equation\" target=\"_blank\" rel=\"noreferrer noopener\">Resolver ecuaciones exponenciales con logaritmos: base 10<\/a>.<\/li>\n\n\n\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=Fl1PvjOh9Us\" target=\"_blank\" rel=\"noreferrer noopener\">Ecuaciones exponenciales ejercicios 1 y 2<\/a>.<\/li>\n\n\n\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=4SyYGHwuktU\" target=\"_blank\" rel=\"noreferrer noopener\">Logaritmos | Soluci\u00f3n de ecuaciones | Ejemplo 3<\/a>.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Las funciones logar\u00edtmicas son muy \u00fatiles cuando se trabaja con fen\u00f3menos que tienen un rango muy amplio de valores, porque te permiten mantener los valores que s\u00ed funcionan en un rango m\u00e1s peque\u00f1o. Las funciones exponenciales son \u00fatiles con fen\u00f3menos que cambian muy r\u00e1pido o que crecen o decaen por un porcentaje en un tiempo en particular.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Las funciones logar\u00edtmicas y exponenciales pueden usarse para modelar situaciones del mundo real. Por ejemplo, podemos usar escalas logar\u00edtmicas para medir las intensidades de terremotos y para crear escala de decibeles del sonido y la escala de pH. La importancia de los logaritmos est\u00e1 en que, gracias a ellos, se facilita la resoluci\u00f3n de c\u00e1lculos muy complejos, lo que ha contribuido enormemente al avance de la ciencia.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"fuentes-de-informacion\">Fuentes de informaci\u00f3n<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Aguilar, A. (2009). Matem\u00e1ticas Simplificadas. (2a ed.). M\u00e9xico: Pearson. Cap. 14, pp. 550 &#8211; 560.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n En 1859, un terrateniente australiano llamado Thomas Austin liber\u00f3 24 conejos en la naturaleza para su caza. Debido a que Australia ten\u00eda pocos depredadores y abundante comida, la poblaci\u00f3n de conejos se dispar\u00f3. En menos de diez a\u00f1os, la poblaci\u00f3n de conejos se contaba por millones. El crecimiento demogr\u00e1fico descontrolado, como en el caso &#8230; <a title=\"Clase digital 10. Ecuaciones exponenciales y logar\u00edtmicas\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-10-ecuaciones-exponenciales-y-logaritmicas\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 10. Ecuaciones exponenciales y logar\u00edtmicas\">Leer m\u00e1s<\/a><\/p>\n","protected":false},"author":142,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","episode_type":"","audio_file":"","podmotor_file_id":"","podmotor_episode_id":"","cover_image":"","cover_image_id":"","duration":"","filesize":"","filesize_raw":"","date_recorded":"","explicit":"","block":"","itunes_episode_number":"","itunes_title":"","itunes_season_number":"","itunes_episode_type":"","footnotes":""},"categories":[83,180,84],"tags":[41,85,86],"class_list":["post-32678","post","type-post","status-publish","format-standard","hentry","category-bachillerato-general","category-cideap","category-algebra-ii","tag-clase-digital","tag-neba04002","tag-sandra-patricia-arriaga-martinez"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/32678","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/users\/142"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/comments?post=32678"}],"version-history":[{"count":17,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/32678\/revisions"}],"predecessor-version":[{"id":32991,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/32678\/revisions\/32991"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=32678"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=32678"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=32678"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}