Answer
$\dfrac {1}{3}\log _{5}\left( x^{2}+1\right) -\log _{5}\left( x^{2}-1\right) $
Work Step by Step
We use the rules of logarithms to obtain:
$\log _{5}\left( \dfrac {\sqrt [3] {x^{2}+1}}{x^{2}-1}\right) =\log _{5} \sqrt [3] {x^{2}+1}-\log \left( x^{2}-1\right) =\log _{5}\left( x^{2}+1\right) ^{\dfrac {1}{3}}-\log _{5}\left( x^{2}-1\right) =\dfrac {1}{3}\log _{5}\left( x^{2}+1\right) -\log _{5}\left( x^{2}-1\right) $
