How do you evaluate ${log}_{\frac{1}{4}} (\frac{1}{4})$ $log_(1/4) (1/4)$ ?

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Answer 1 · 2016-07-27T19:14:19

${log}_{\frac{1}{4}} (\frac{1}{4}) = 1$ $log_(1/4) (1/4) = 1$

For any base $b > 0$ $b > 0$ with $b \neq 1$ $b != 1$ we have:

${log}_{b} b = 1$ $log_b b = 1$

$b = \frac{1}{4}$ $b=1/4$ is no exception.

If you like, use the change of base formula:

${log}_{a} b = \frac{{log}_{c} b}{{log}_{c} a}$ $log_a b = (log_c b)/(log_c a)$

So we find:

${log}_{\frac{1}{4}} (\frac{1}{4}) = \frac{log (\frac{1}{4})}{log (\frac{1}{4})} = 1$ $log_(1/4) (1/4) = (log (1/4))/(log (1/4)) = 1$

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