Answer
$log_{4}(x+5)-2log_{4}x$
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, $log_{4}\frac{x+5}{x^{2}}= log_{4}(x+5)-log_{4}x^{2}$.
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_{4}(x+5)-log_{4}x^{2}= log_{4}(x+5)-2log_{4}x$.
