Question

O valor de log $\frac{32}{243} / \frac{9}{4}$ é: ?

Answer 1

$log_{(\frac{9}{4})}\left(\dfrac{32}{243}\right)=x\\\\\\\left(\dfrac{9}{4}\right)^{x}=\left(\dfrac{32}{243}\right)\\\\\\\left(\dfrac{3^{2}}{2^{2}}\right)^{x}=\dfrac{2^{5}}{3^{5}}\\\\\\\left(\left[\dfrac{3}{2}\right]^{2}\right)^{x}=\left(\dfrac{2}{3}\right)^{5}\\\\\\\left(\dfrac{3}{2}\right)^{2x}=\left(\dfrac{3}{2}\right)^{-5}$

Bases iguais, iguale os expoentes:

$2x=-5\\\\\\\boxed{\boxed{x=-\dfrac{5}{2}}}$