Question

(3/5)^2x=125/27 equação exponencial

Answer 1

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

Espero ter ajudado.

Answer 2

$\left( \dfrac{3}{5} \right)^{2x} = \dfrac{125}{27} \to~~~~ \left( \dfrac{3}{5} \right)^{2x} = \dfrac{5}{3}^3 \to~~~~ \left( \dfrac{3}{5} \right)^{2x} = \dfrac{3}{5}^{-3} \to~~~~ \\\\\\Elimine~~~as~~~bases:\\\\\\ 2x = -3\to~~~~ \large\boxed{x = - \dfrac{3}{2}}$