Calculus 8th Edition

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

Chapter 6 - Inverse Functions - Review - Exercises - Page 505: 16


$$x =\ln\frac{1}{e^3-1}$$

Work Step by Step

Given $$\ln (1+e^{-x})=3$$ Then \begin{align*} \ln (1+e^{-x})&=3\\ 1+e^{-x}&=e^3\\ e^{-x}&=e^3-1\\ \ln e^{-x}&=\ln (e^3-1)\\ -x&=\ln (e^3-1)\\ x&=\ln (e^3-1)^{-1}\\ &=\ln\frac{1}{e^3-1} \end{align*}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.