Answer
$log_{7}\frac{x+9}{x^{2}+10}$
Work Step by Step
We know 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, $log_{7}(x+9)-log_{7}(x^{2}+10)=log_{7}\frac{x+9}{x^{2}+10}$.