Question

[(2/5) ^{x-1=125/8
?????

Answer 1

Olá,

use a propriedade da exponenciação:

$\dfrac{a}{b}^c~\to~ \dfrac{b}{a}^{-c}\\\\ \dfrac{2}{5}^{x-1}= \dfrac{125}{8}\\\\ \dfrac{2}{5}^{x-1}= \dfrac{5^3}{2^3}\\\\ \dfrac{2}{5}^{x-1}= \dfrac{5}{2}^3\\\\ \dfrac{2}{5}^{x-1}= \dfrac{2}{5}^{-3}~\to~elimina~as~bases~e~conserva~os~expoentes:\\\\ x-1=-3\\ x=-3+1\\ x=-2\\\\ \boxed{S=\{-2\}}$