Answer
$$x=3\left(2+\sqrt{2}\right)$$
Work Step by Step
Using the rules of logarithms to solve the equation, we find:
$$\log _3\left(\left(x-9\right)\left(x-3\right)\right)=2 \\ \log _3\left(\left(x-9\right)\left(x-3\right)\right)=\log _3\left(9\right) \\ x=3\left(2+\sqrt{2}\right),\:x=3\left(2-\sqrt{2}\right)$$
Checking for extraneous solutions, we see that only $x=3\left(2+\sqrt{2}\right)$ is valid.
