If log4 (x) = 12 , then log2 (x/4) is equal to what?

We'll consider the constraint and we'll take
antilogarithm:

log4 (x) = 12 => x =
4^12

We'll substitute x by 4^12 in the
fraction:

log2 (x/4) = log2
(4^12/4)

Since the exponentials have matching bases, we'll
subtract exponents:

4^12/4 = 4^(12-1) =
4^11

log2 (4^12/4) = log2
(4^11)

We'll use power rule of
logarithms:

log2 (4^11) = 11log2
(4)

But 4 = 2^2

11log2 (2^2) =
22 log2 (2)

But log2 (2) = 1 => 22 log2 (2) =
22

Therefore, log2 (x/4) =
22.