Solve the equation log 3(x-8)=2.

Before solving the equation, which is a logarithmical equation, we have to find out the restrictive domain for the x values.

For this reason, we have to impose the condition that x-8>0.

x>8, that means that x belongs to the interval (8, +inf).

Now, we can solve the equation:

x-8=3^2

x-8=9

x=9+8

x=17

The solution is acceptable because is belonging to the interval of allowed x values.