Answer
$\displaystyle \ln 9+\frac{1}{3}\ln 5-\frac{1}{4}\ln 3$
Work Step by Step
$\displaystyle \ln\frac{9\cdot\sqrt[3]{5}}{\sqrt[4]{3}}=$
...Apply rule: $\displaystyle \log_{a}\frac{x}{y}=\log_{a}x-\log_{a}y$
$=\ln(9\cdot\sqrt[3]{5})-\ln(\sqrt[4]{3})$
...Apply rule: $\log_{a}xy=\log_{a}x+\log_{a}y$
$=\ln 9+\ln\sqrt[3]{5}-\ln(\sqrt[4]{3})$
... $\sqrt[3]{5}=5^{1/3},\qquad \sqrt[4]{3}=3^{1/4}$
$=\ln 9+\ln 5^{1/3}-\ln 3^{1/4}$
... Apply rule:$ \log_{a}x^{r}=r\log_{a}x$
$=\displaystyle \ln 9+\frac{1}{3}\ln 5-\frac{1}{4}\ln 3$
