Answer
$\displaystyle \ln\sqrt[3]{\frac{x(x+3)^{2}}{(x^{2}-1)}}$
Work Step by Step
See Th.5.2.
Property $1$ : $\ln(1)=0$
Property $2$ : $\ln(ab)=\ln a + \ln b$
Property $3$ : $\ln(a^{n})=n\cdot\ln a $
Property 4 : $\displaystyle \ln(\frac{a}{b})=\ln a - \ln b$
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$\displaystyle \frac{1}{3}[2\ln(x+3)+\ln x-\ln(x^{2}-1)]$= ... property $3$...
$=\displaystyle \frac{1}{3}[\ln(x+3)^{2}+\ln x-\ln(x^{2}-1)]$= ... property $2$...
$=\displaystyle \frac{1}{3}[\ln[(x+3)^{2}\cdot x]-\ln(x^{2}-1)]$= ... property $4$...
$=\displaystyle \frac{1}{3}\cdot\ln\left[\frac{x(x+3)^{2}}{(x^{2}-1)}\right]$= ... property $3$...
$=\displaystyle \ln\left[\frac{x(x+3)^{2}}{(x^{2}-1)}\right]^{1/3}$
$=\displaystyle \ln\sqrt[3]{\frac{x(x+3)^{2}}{(x^{2}-1)}}$
