Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.1 Exercises: 25

Answer

$\displaystyle \frac{1}{2}\ln(x-1)-\frac{1}{2}\ln x$

Work Step by Step

See Th.5.2. Property $3$ : $\ln(a^{n})=n\cdot\ln a $ Property 4 : $\displaystyle \ln(\frac{a}{b})=\ln a - \ln b$ $\displaystyle \ln\sqrt{\frac{x-1}{x}}=\ln(\frac{x-1}{x})^{1/2}$= ... property $3$... $=\displaystyle \frac{1}{2}\ln(\frac{x-1}{x})$= ... property $4$... $=\displaystyle \frac{1}{2}[\ln(x-1)-\ln x]$ $=\displaystyle \frac{1}{2}\ln(x-1)-\frac{1}{2}\ln x$
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