Question

Como resolver a função exponencial: (5/3)^(2x) = 27/125

Answer 1

$\left(\frac{5}{3}\right)^{2x}= \frac{27}{125} \\ \\ \left( \frac{5}{3}\right) ^{2x}=\left( \frac{125}{27}\right)^{-1} \\ \\ \left(\frac{5}{3}\right)^{2x}= \left(\frac{5^3}{3^3}\right)^{-1} \\ \\ \left( \frac{5}{3}\right)^{2x}= \left(\frac{5}{3}\right)^{-3}$

Bases iguais, expoentes iguais:

$2x=-3 \\ \\ \boxed{x=- \frac{3}{2} }$