Answer
$\ln\sqrt[3]{\frac{(x+6)^{5}}{x(x^{2}-25)}}$
Work Step by Step
$\displaystyle \frac{1}{3}[5\ln(x+6)-\ln x-\ln(x^{2}-25)]$
... move the $5$ in the first term by applying the power rule
$=\displaystyle \frac{1}{3}[\ln(x+6)^{2}-(\ln x+\ln(x^{2}-25))]$
... apply the product rule
$=\displaystyle \frac{1}{3}\{\ln(x+6)^{2}-\ln[x(x^{2}-25)]\}$
... apply the quotient rule
$=\displaystyle \frac{1}{3}\ln[\frac{(x+6)^{5}}{x(x^{2}-25)}]$
... move the $\displaystyle \frac{1}{3}$ by applying the power rule
$=\displaystyle \ln[\frac{(x+6)^{5}}{x(x^{2}-25)}]^{1/3}$
... write the rational exponent as a root (optional)
$=\ln\sqrt[3]{\frac{(x+6)^{5}}{x(x^{2}-25)}}$
