Answer
$3log_{5}x+log_{5}(x+1)$
Work Step by Step
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, $log_{5}x^{3}(x+1)=log_{5}x^{3}+log_{5}(x+1)$.
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, $log_{5}x^{3}+log_{5}(x+1)=3log_{5}x+log_{5}(x+1)$.