If Log 4 (x) = 12, then log 2 (x / 4) is equal to what?

Given that log 4 (x) = 12

We
need to find the values of log2 (x/4)

Let us use the
logarithm properties to simplify.

We know that log a/b =
log a - log b

==> log2 (x/4) = log2 x - log2
4

But log2 4 = log2 2^2 = 2*log2 2 =
2

==> log2 (x/4) = log2 x -
2.............(1)

Now we are given that log4 x =
12

We will rewrite.

==>
log4 x = log2 x / log2 4 = log2 x/ 2 = (1/2)log2 x=
12

==> log2 x = 2*12 =
24

==> log2 x/4 = 24 -2 =
22

Then the values of log2 (x/4) =
22