If Log 4 (x) = 12, then log 2 (x / 4) is equal to what?
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calendarEducator since 2010
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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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calendarEducator since 2008
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starTop subjects are Math, Science, and Social Sciences
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