Question

Encontre o valor de x:

Answer 1

$\displaystyle \sf \left(\frac{4}{25}\right)^x=\left(\frac{125}{8}\right) \\\\\\ \left(\frac{2^2}{5^2}\right)^x = \left(\frac{5^3}{2^3}\right)\\\\\\ \left(\frac{2}{5}\right)^{2. x} =\left(\frac{2}{5}\right)^{-3} \\\\ J\'a \ que\ as \ bases\ s\~ao\ iguais \ podemos\ igualar\ os \ expoentes : \\\\ 2x=-3 \\\\ \boxed{\sf x = \frac{-3}{2}}\checkmark$