College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.5 - Exponential and Logarithmic Equations - 4.5 Exercises - Page 447: 73



Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ \ln e^x-2\ln e=\ln e^4 ,$ use the properties of logarithms to combine the logarithmic expressions. Then use the properties of equality to solve for the variable. Finally, do checking of the solution/s with the original equation. $\bf{\text{Solution Details:}}$ Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the equation above is equivalent \begin{array}{l}\require{cancel} x\ln e-2\ln e=4\ln e .\end{array} Since $\ln e=1,$ the equation above is equivalent to \begin{array}{l}\require{cancel} x(1)-2(1)=4(1) \\\\ x-2=4 \\\\ x=4+2 \\\\ x=6 .\end{array} Upon checking, $ x=6 $ satisfies the original equation.
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