# How do you evaluate log_(1/4) (1/4)?

Jul 27, 2016

${\log}_{\frac{1}{4}} \left(\frac{1}{4}\right) = 1$

#### Explanation:

For any base $b > 0$ with $b \ne 1$ we have:

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

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

If you like, use the change of base formula:

${\log}_{a} b = \frac{{\log}_{c} b}{{\log}_{c} a}$

So we find:

${\log}_{\frac{1}{4}} \left(\frac{1}{4}\right) = \frac{\log \left(\frac{1}{4}\right)}{\log \left(\frac{1}{4}\right)} = 1$