Given:

To solve it, follow the steps below.
Step 01: Use the given hint (512 = 32*16).

Step 02: Use the product rule for logarithms.
According to the product rule:

Then,

Step 03: Use the definition of the log to solve the problem.
Given the definition:

So, let's solve each part of the equation.

In order to find x, let's factor 32.
32 | 2
16 | 2
8 | 2
4 | 2
2 | 2
1
2⁵ = 32

And,

Now, let's solve the second term.

Let's factor 16:
16 | 2
8 | 2
4 | 2
2 | 2
1
2⁴ = 16
Substituting it in the equation:

Then,

Step 04: Substitute the solutions and solve the equations.

Answer: 9.