Question

ecuaciones exponenciales resolver​

Answer 1

Respuesta:

x = 16

Explicación paso a paso:

aplicamos la ley de exponentes

$25^{(x-1)\frac{1}{5}} = 5^{(x+2)\frac{1}{3}}$

convertimos $25^{\left(x-1\right)\frac{1}{5}}$ a base 5

$5^{2*(x-1)*\frac{1}{5}} = 5^{\left(x+2)\frac{1}{3}}$

$2*(x-1)*\frac{1}{5}} = (x+2)*\frac{1}{3}}$      simplificamos

$\frac{2}{5}*(x-1)= (x+2)*\frac{1}{3}}$

$\frac{2}{5}x-\frac{2}{5}=\frac{1}{3}x+\frac{2}{3}$       sumamos a ambos lados

$\frac{2}{5}x-\frac{2}{5}+\frac{2}{5}=\frac{1}{3}x+\frac{2}{3}+\frac{2}{5}$   simplificamos

$\frac{2}{5}x=\frac{16}{15}+\frac{1}{3}x$  restamos a ambos lados

$\frac{2}{5}x-\frac{1}{3}x=\frac{16}{15}+\frac{1}{3}x-\frac{1}{3}x$   simplificamos

$\frac{1}{15}x=\frac{16}{15}$

$15*\frac{1}{15}x$ = (16*15)/15  despejamos X

x = 16