Answer
$3log_{5}x+log_{5}(x+1)$
Work Step by Step
The product property of logarithms tells us that $log_{b}xy=log_{b}x+log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$).
Therefore, $log_{5}x^{3}(x+1)= log_{5}x^{3}+log_{5}(x+1)$.
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, $ log_{5}x^{3}+log_{5}(x+1)=3log_{5}x+log_{5}(x+1)$.
