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

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We have log(4) x = 12. We need to find log(2) (x/4)

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

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

use log a^b = a*log b

=> log(2) x - 2 ...(1)

log(4) x = 12

=> x = 4^12

=> x = 2^2^12

=> x = 2^24

take log to base 2 of both the sides

=> log(2) x = 24

Substituting in (1)

log(2) x - 2

=> 24 - 2

=> 22

The required value of log(2)(x/4) = 22

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log4 (x) = 12

We will use logarithm properties to simplify.

We will rewrite:

 ==> log4 x = log2 x/log2 4 = log2 x / 2 = 12

 ==> log2 x = 2*12 = 24

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

                     = log2 x - log2 2^2

                       = log2 x - 2

                         = 24 -2 = 22

==> log2 (x/4) = 22

Approved by eNotes Editorial Team
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