Answer
$\frac{1}{5}\cdot (a+b)$
Work Step by Step
Recall:
(1) $\sqrt[m]{a}=a^{\frac{1}{m}}$
(2) $\log_a {x^n}=n\cdot \log_a {x}$.
(3) $\log_a{xy}=\log_a{x} +\log_a{y}$
Use rule (1) above to obtain
$\ln{\sqrt[5]{6}}=\ln{(6^{\frac{1}{5}})}$
Use rule (2) above to obtain
$\ln{(6^{\frac{1}{5}})}=\frac{1}{5}\cdot \ln {6}.$
Use rule (3) above to obtain
$\frac{1}{5}\cdot \ln {6}
\\=\frac{1}{5}\cdot \ln {(2\cdot3)}
\\=\frac{1}{5}\cdot (\ln {2}+\ln{3})
\\=\frac{1}{5}\cdot (a+b).$
