Answer
$ \log_{4}[\sqrt[3]{\dfrac{x}{y}}\cdot(x+1)^{2}]$
Work Step by Step
$\displaystyle \frac{1}{3}(\log_{4}x-\log_{4}y)+2\log_{4}(x+1)$
... apply quotient rule for the first term, power rule for the second
$=\displaystyle \frac{1}{3}\log_{4}(\frac{x}{y})+\log_{4}(x+1)^{2}$
... apply power rule for the first term
$=\displaystyle \log_{4}(\frac{x}{y})^{1/3}+\log_{4}(x+1)^{2}$
... apply product rule
$=\displaystyle \log_{4}[(\frac{x}{y})^{1/3}(x+1)^{2}]$
$=\log_{4}[\sqrt[3]{\frac{x}{y}}\cdot(x+1)^{2}]$
