Answer
$log_{7}9+2log_{7}x-log_{7}y $
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, $log_{7}\frac{9x^{2}}{y}=log_{7}9x^{2}-log_{7}y$.
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_{7}9x^{2}-log_{7}y= log_{7}9+log_{7}x^{2}-log_{7}y $.
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_{7}9+log_{7}x^{2}-log_{7}y= log_{7}9+2log_{7}x-log_{7}y $.
