Answer
$=\dfrac {2}{3}\left( 2\ln \left( x-4\right) -\ln \left( x^{2}-1\right) \right) $
Work Step by Step
We use the rules of logarithms to obtain:
$\ln \left[ \dfrac {\left( x-4\right) ^{2}}{x^{2}-1}\right] ^{2/3}=\dfrac {2}{3}\ln \dfrac {\left( x-4\right) ^{2}}{x^{2}-1}=\dfrac {2}{3}\left( \ln \left( x-4\right) ^{2}-\ln \left( x^{2}-1\right) \right) =\dfrac {2}{3}\left( 2\ln \left( x-4\right) -\ln \left( x^{2}-1\right) \right) $