Answer
$log_{5}\frac{x^{3}}{y^{5}}$
Work Step by Step
The power property of logarithms tells us that $log_{b}x^{r}=r log_{b}x$ (where x and b are positive real numbers, $b\ne1$, and r is a real number).
Therefore, $3log_{5}x-5log_{5}y=log_{5}x^{3}-log_{5}y^{5}$.
The quotient property of logarithms tells us that $log_{b}\frac{x}{y}=log_{b}x-log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$).
Therefore, $ log_{5}x^{3}-log_{5}y^{5}=log_{5}\frac{x^{3}}{y^{5}}$.
