Log 4 (2x-16) = 4

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

2x-16>0

We'll
add 16 both
sides:

2x>16

We'll
divide by
2:

x>8

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

Now, we'll solve the
equation:

2x-16= 4^4

2x-16 =
256

We'll add 16 both
sides:

2x = 16+256

2x =
272

We'll divide by
2:

x =
136

The solution is admissible because the
value belongs to the interval (8,+inf.)