College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.5 - Properties of Logarithms - 6.5 Assess Your Understanding - Page 460: 103


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Work Step by Step

We know that if $e^x=y$, then $ln y=x$, hence $2x=\ln(e^{2x}).$ We know that $\log_a x+\log_a y=\log_a (x\cdot y)$, hence $2x+\ln(1+e^{-2x})=\ln(e^{2x})+\ln(1+e^{-2x})=\ln(e^{2x}\cdot(1+e^{-2x}))=\ln(e^{2x}+e^{2x-2x})=\ln(e^{2x}+1).$
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