Answer
$\dfrac{1}{3}$
Work Step by Step
We are asked to evaluate:
$\log_{64}{4}$
Recall the power property of logarithms (pg. 462):
$\log_b{m^n}=n\log_b{m}$
Using this property, we get:
$\log_{64}{4}=\log_{64}{64^{1/3}}=\frac{1}{3}\log_{64}{64}=\frac{1}{3}\times 1=\frac{1}{3}$
Here we used the fact that $64^{1/3}=4$ (since $4^3=64$).
We also used the fact that $\log_{64}{64}=1$ (because $64^1=64$).
