9. Solve for x and check:

First combine a a single log.

Now we can change to exponential notation.

Simplify. Remove parentheses on the left and compute the power on the right.

This gives us a quadratic. Transpose everything to one side, leaving a 0 on the other and hope that it factors.

It does

Set the factors = 0 and solve.

We must now check the solutions. If x = 3, the eauation becomes

and it checks. For the other solution, let x = -4

Here we are being asked to take logs of negative numbers, so the solution doesn't check.

The only solution, then, is