Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.3 Logarithmic Functions - 6.3 Exercises - Page 426: 10


ln$\sqrt[10] \frac{x-1}{x+1}=\frac{1}{10}[ln(x-1)-ln(x+1)]$

Work Step by Step

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