Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 28



Work Step by Step

Using the properties of equality, the given equation, $ 4+5e^{-x}=9 ,$ is equivalent to \begin{array}{l}\require{cancel} 5e^{-x}=9-4 \\\\ 5e^{-x}=5 \\\\ e^{-x}=\dfrac{5}{5} \\\\ e^{-x}=1 .\end{array} Taking the natural logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the equation, $ e^{-x}=1 ,$ is \begin{array}{l}\require{cancel} \ln e^{-x}=\ln 1 \\\\ -x(\ln e)=\ln 1 \\\\ -x(1)=\ln 1 \\\\ -x=\ln 1 \\\\ x=-\ln 1 \\\\ x=0 .\end{array}
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