## Precalculus (10th Edition)

$C$
Recall that in $f(x)=\log_a{x}, x \gt 0$. Thus, in the given function, $x+2$ must be greater than $0$. Hence, $x+2\gt 0$. Subtracting $2$ from both sides gives $x\gt -2$. Therefore, the correct answer is $C$.