Answer
$log_{a}\frac{rt^{3}}{s}$
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, $(log_{a}r-log_{a}s)+3log_{a}t=(log_{a}r-log_{a}s)+log_{a}t^{3}$.
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, $(log_{a}r-log_{a}s)+log_{a}t^{3}=log_{a}\frac{r}{s}+log_{a}t^{3}$.
We know that $log_{b}xy=log_{b}x+log_{b}y$ (where $x$, $y$, and $b$ are positive real numbers and $b\ne1$).
Therefore, $log_{a}\frac{r}{s}+log_{a}t^{3}=log_{a}\frac{r\times t^{3}}{s}=log_{a}\frac{rt^{3}}{s}$.