Answer
$2log_{3}(x+5)-log_{3}x $
Work Step by Step
The quotient property of logarithms tells us 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, $log_{3}\frac{(x+5)^{2}}{x}= log_{3}(x+5)^{2}-log_{3}x$.
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_{3}(x+5)^{2}-log_{3}x = 2log_{3}(x+5)-log_{3}x $.
