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

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If Log 4 (x) = 12, then log 2 (x / 4)

Let us try and rewrite log 2 (x/4)

log 2 (x/4) = log 2 (1/4)*x

We that log ab = log a + log b

==> loh 2 (x/4) = log 2 (1/4) + log 2 (x)

                         = log 2 (4)^-1 + log 2 (x)

                          = log 2 (2)^-2 + log 2 x

                          = -2log 2 2 + log 2 x

                           = -2 + log 2 x

But we are given that log 4 x = 12

==> x = 4^12 = (2^2)^12  = 2^(24)

==> x = 2^24

==> log 2 x = 24

==> log 2 (x/4) = -2 + log 2 x

                             = -2 + 24 = 22

==> log 2 (x/4) = 22

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