How do you evaluate $log_16(1/4)$ ?

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Answer 1 · 2016-03-23T14:01:34

$x=-1/2$

Let $log_16(1/4)=x$ , then $16^x=1/4$ or

$(2^4)^x=1/(2^2)$ or

$2^(4x)=2^(-2)$

Hence $4x=-2$ i.e. $x=-2/4=-1/2$

Answer 2 · 2016-03-23T14:10:13

Let's write it in exponential form.

$log_ab = x -> a^x = b$

$log_16(1/4) = x -> 16^x = 1/4$

Solve for x by putting everything in the same base.

$(2^4)^x = 1/(2^2)$

$2^(4x) = 2^(-2)$

$x = -1/2$

Therefore, $log_16(1/4) = -1/2$

Practice exercises:

a). $log_9(1/27)$

b) $log_x(81)= 4$

c) $log_(2x + 1)11x = 2$

Good luck!

How do you evaluate log_16(1/4)log_16(1/4)?