Answer
$\frac{2}{3}$
Work Step by Step
Since $25=5^2$, the given expression is equivalent to:
$=\log_5{(\sqrt[3]{5^2})}$
RECALL:
$\sqrt[n]{a^m} = a^{\frac{m}{n}}, a \ge 0$
Use the rule above to obtain:
$\log_{5}{(\sqrt[3]{5^2})}=\log_{5}{(5^{\frac{2}{3}})}$
RECALL:
$\log_a{(a^n)} = n, a \gt0, a\ne1$
Using the rule above gives:
$\log_{5}{(5^{\frac{2}{3}})}=\frac{2}{3}$
Thus,
$\log_{5}{\sqrt[3]{25}}=\frac{2}{3}$
