## Calculus 8th Edition

ln$\sqrt[10] \frac{x-1}{x+1}=\frac{1}{10}[ln(x-1)-ln(x+1)]$
Use logarithmic properties $ln(pq) = lnp+lnq$ and $ln(p)^{m}= m lnp$ Consider the quantity ln$\sqrt[10] \frac{x-1}{x+1}$ as follows: ln$\sqrt[10] \frac{x-1}{x+1}=\ln[\frac{(x-1)}{(x+1)}]^{\frac{1}{10}}$ This implies ln$\sqrt[10] \frac{x-1}{x+1}=\frac{1}{10}\ln[\frac{(x-1)}{(x+1)}]$ Hence, ln$\sqrt[10] \frac{x-1}{x+1}=\frac{1}{10}[ln(x-1)-ln(x+1)]$