Answer
$\ln\sqrt[3]{\dfrac{(x+5)^{2}}{x(x^{2}-4)}}$
Work Step by Step
$\displaystyle \frac{1}{3}[2\ln(x+5)-\ln x-\ln(x^{2}-4)]=$
... move the 2 in the first term by applying the power rule
$=\displaystyle \frac{1}{3}[\ln(x+5)^{2}-\ln x-\ln(x^{2}-4)]$
... apply the quotient rule
$=\displaystyle \frac{1}{3}[\ln\frac{(x+5)^{2}}{x}-\ln(x^{2}-4)]$
... apply the quotient rule again
$=\displaystyle \frac{1}{3}\cdot\ln[\frac{(x+5)^{2}}{x(x^{2}-4)}]$
... move the $\displaystyle \frac{1}{3}$ by applying the power rule
$=\displaystyle \ln[\frac{(x+5)^{2}}{x(x^{2}-4)}]^{1/3}$
... write the rational exponent as a root (optional)
$=\ln\sqrt[3]{\dfrac{(x+5)^{2}}{x(x^{2}-4)}}$
