Solve the equation log 4 (x-8) = 2 .

Before solving the equation, we have to impose constraints
of existance of logarithm
function.

x-8>0

We'll
add 8 both
sides:

x>8

So, in order
to exist, the values of x have to be in the interval (8,
+inf.)

Now, we'll solve the
equation:

x-8 = 4^2

x-8 =
16

We'll add 8 both sides:

x =
16+8

x =
24

The solution is admissible because is in
the interval (8,+inf.).