Answer
$= \frac{2}{3}log_5(x)+\frac{1}{3}log_5(y) - \frac{2}{3}$
Work Step by Step
$= log_5(\sqrt[3] {\frac{x^{2}y}{25}})$
$= log_5(\frac{x^{2}y}{25})^{\frac{1}{3}}$
$= \frac{1}{3}log_5(\frac{x^{2}y}{25})$
$= \frac{1}{3}log_5(x^{2}y) - \frac{1}{3}log_5(25)$
$=\frac{1}{3}log_5(x^{2})+\frac{1}{3}log_5(y) - \frac{1}{3}log_5(5^{2})$
$= \frac{2}{3}log_5(x)+\frac{1}{3}log_5(y) - \frac{2}{3}log_5(5)$
$= \frac{2}{3}log_5(x)+\frac{1}{3}log_5(y) - \frac{2}{3}$
