Answer
$\dfrac{1}{4}(a-b)$
Work Step by Step
Recall:
(1) $\sqrt[m]{a}=a^{\frac{1}{m}}$
(2) $\log_a {x^n}=n\cdot \log_a {x}$.
(3) $\log_a{xy}=\log_a{x} +\log_a{y}$
(4) $\log_a{\frac{x}{y}}=\log_a{x} -\log_a{y}$
Use rule (1) to obtain
$\ln {\sqrt[4] {\frac{2}{3}}}=\ln {\frac{2}{3}}^{\frac{1}{4}}=\dfrac{1}{4}\cdot \ln {\frac{2}{3}}.$
Use rule (4) to obtain
$\dfrac{1}{4}\cdot \ln {\frac{2}{3}}=\dfrac{1}{4}\cdot \left(\ln {2}-\ln{3}\right)=\dfrac{1}{4}(a-b)$
