Answer
$log_{a}\frac{125}{3}$
Work Step by Step
We know that $log_{b}x^{r}=rlog_{b}x$ (where $x$ and $b$ are positive real numbers, $b\ne1$, and $r$ is a real number).
Therefore, $3log_{a}5-\frac{1}{2}log_{a}9=log_{a}5^{3}-log_{a}9^{\frac{1}{2}}$.
We know 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, $log_{a}5^{3}-log_{a}9^{\frac{1}{2}}=log_{a}\frac{5^{3}}{9^{\frac{1}{2}}}=log_{a}\frac{125}{3}$.