Answer
$\dfrac{1}{5}(b+a)$
Work Step by Step
$\ln \sqrt[5]{6} = \ln 6^{\frac{1}{5}}$
$\because \log_a M^r = r \log_a M$
$\therefore \ln 6^{\frac{1}{5}} = \frac{1}{5} \ln{6}$
$\because \log_a (MN) = \log_a M+\log_a N$
$\therefore \ln6 = \ln(3 \cdot 2)= \ln3+\ln2$
With $\ln3 = b \hspace{20pt} \text{and} \hspace{20pt} \ln2=a$, then
$\ln3+\ln2 = b+a$
$\ln6 = b+a$
Therfeore,
$\ln \sqrt[5]{6} =\frac{[1}{5}\ln{6} = \boxed{\dfrac{1}{5}(b+a)}$
