If log4 (x) = 12 , what is log2 (x/4) ?
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Given that log(4) x = 12
We need to find log(2) x/4
First we will use logarithm properties to simplify.
We know that:
log a/b = log a - log b
==> log2 (x/4) = log2 x - log2 4
Now we will rewrite 4= 2^2
==> log2 (x/4) = log2 x - log2 2^2
Now we know that log a^b = b*log a
==> log2 (x/4) = log2 x - 2log2 2
But log2 2 = 1
==> log2 (x/4) = log2 x - 2
Now we will rewrite log2 x = log4 x / log4 2
= log4 x / log4 (4^1/2)
= log4 x / 1/2 = 2log4 x
==> log2 (x/4) = 2log4 x -2
\But log4 x = 12
==> log2 (x/4) = 2*12 -2 = 22
==> log2 (x/4) = 22
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