## Precalculus (6th Edition) Blitzer

$\log_{4}[\sqrt[3]{\dfrac{x}{y}}\cdot(x+1)^{2}]$
$\displaystyle \frac{1}{3}(\log_{4}x-\log_{4}y)+2\log_{4}(x+1)$ ... 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 $=\displaystyle \log_{4}[(\frac{x}{y})^{1/3}(x+1)^{2}]$ $=\log_{4}[\sqrt[3]{\frac{x}{y}}\cdot(x+1)^{2}]$