# How do you evaluate log_4 1/64?

Jul 9, 2015

${\log}_{b} 1 = 0$, for any base.

#### Explanation:

So we get $\frac{1}{64}$

Jul 9, 2015

If the question was intended to be: Find ${\log}_{4} \left(\frac{1}{64}\right)$, then the answer is $- 3$.

#### Explanation:

Remember that the log base 4 of a number is the exponent needed on 4 to get that number.

$\frac{1}{64} = \frac{1}{4} ^ 3 = {4}^{- 3}$

Now what exponent do I need to put on 4, in order to get ${4}^{- 3}$?

(Yes, it is a self-answering question. It's fun to think of other self-answering questions. OK, it might be nerdy fun.)

${\log}_{4} {4}^{- 3} = - 3$