Answer
$\log_{64}{4}=\frac{1}{3}$
Work Step by Step
RECALL:
(i) $\sqrt[n]{a}=a^{\frac{1}{n}}.$
(ii) $b^y=x \longleftrightarrow \log_b{x} =y .$
Use rule (i) above to obtain
$64^{\frac{1}{3}}=4.$
Use rule (ii) above to obtain
$64^{\frac{1}{3}} = 4 \longrightarrow \log_{64}{4}=\frac{1}{3}.$
Thus, the equivalent logarithmic form of the given expression is
$\log_{64}{4}=\frac{1}{3}.$
