## College Algebra (10th Edition)

$\frac{2}{3}$
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, $\log_{5}{\sqrt[3]{25}}=\frac{2}{3}$