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

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have log (4) x = 12

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

log(4) x = 12

=> log(2) x / log(2) 4 = 12

=> log(2) x / 2* log(2) 2 = 12

=> log(2) x / 2 = 12

=> log(2) x = 24

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

=> 24 - 2 = 22

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

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