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


Dec 22nd, 2014

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.


Dec 22nd, 2014

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