Answer
$x=7$
Work Step by Step
We are given that $9=3^{x-5}$. Both of these numbers are powers of 3, so we can rewrite the equation as $3^{2}=3^{x-5}$.
From the uniqueness of $b^{x}$, we know that $b^{x}=b^{y}$ is equivalent to $x=y$ (when $b\gt0$ and $b\ne1$).
Therefore, $2=x-5$. To solve for x, add 5 to both sides.
$x=7$
