Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Section 7.2 - Natural Logarithms - Exercises 7.2 - Page 381: 4


(a) $0$ (b) $ \ln {(2x+1)}$ (c) $\ln (t-1)$

Work Step by Step

(a) \begin{align*} \ln \sec \theta+\ln \cos \theta&=\ln \sec \theta \cos \theta\\ &= \ln (1)=0 \end{align*} (b) \begin{align*} \ln (8 x+4)-2 \ln 2&=\ln (8 x+4)-\ln 2^2\\ &= \ln \frac{8x+4}{4}\\ &= \ln {(2x+1)} \end{align*} (c) \begin{align*} 3 \ln \sqrt[3]{t^{2}-1}-\ln (t+1)&= \ln {t^{2}-1}-\ln (t+1)\\ &= \ln \frac{ t^2-1}{t+1 }\\ &= \ln \frac{(t-1)(t+1)}{t+1}\\ &= \ln (t-1) \end{align*}
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