If log4 (x) = 12 , then log2 (x/4) is equal to what?
3 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
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
hala718 | High School Teacher | (Level 1) Educator Emeritus
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
giorgiana1976 | College Teacher | (Level 3) Valedictorian
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.