Answer
ln$\sqrt[3] \frac{x-1}{x+1}=\frac{1}{3}[ln(x-1)-ln(x+1)]$
Work Step by Step
Use logarithmic properties $ln(pq) = lnp+lnq$ and $ln(p)^{m}= m lnp$
Consider the quantity ln$\sqrt[3] \frac{x-1}{x+1}$ as follows:
ln$\sqrt[3] \frac{x-1}{x+1}=\ln[\frac{(x-1)}{(x+1)}]^{\frac{1}{3}}$
This implies
ln$\sqrt[3] \frac{x-1}{x+1}=\frac{1}{3}\ln[\frac{(x-1)}{(x+1)}]$
ln$\sqrt[3] \frac{x-1}{x+1}=\frac{1}{3}[ln(x-1)-ln(x+1)]$