log 4 (2x-16) = 4

Let us rewrite :

(2x -16) = 4^4

2x -16 = 256

Now add 16 to both sides:

==> 2x = 272

==> x = 272/2 = 136

Let us check:

log 4 (2(136)-16) = 4

log 4 ( 272-16) = 4

log 4 (256) = 4

log 4 (4^4) = 4

4log 4 = 4

4= 4

Then the solution is x = 136

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.)

log 4 (2x-16) = 4

Solution:

If log a (b) = x, then b = a^x.

Therefore

2x-16 = 4^4

2x = 16+4^4 = 16+256 = 272

x = 272/2 = 136