Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 5 - Logarithmic Functions - 5.1 Logarithms and Their Properties - Exercises and Problems for Section 5.1 - Exercises and Problems - Page 195: 63



Work Step by Step

Using the properties of logarithms, we find: $$\ln \left(e^{x+5}\right)=\ln \left(7\cdot \:2^x\right) \\ \left(x+5\right)\ln \left(e\right)=\ln \left(7\right)+x\ln \left(2\right) \\ x+5=\ln \left(7\right)+x\ln \left(2\right) \\ x=\frac{\ln \left(7\right)-5}{1-\ln \left(2\right)} \\ x=-9.95$$
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