Answer
$log_{a}\frac{125}{81}$
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, $3log_{a}5-4log_{a}3=log_{a}5^{3}-log_{a}3^{4}$.
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, $log_{a}5^{3}-log_{a}3^{4}=log_{a}\frac{5^{3}}{3^{4}}=log_{a}\frac{125}{81}$.
