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: 36

Answer

$x=e^3$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ 3\ln x=9 ,$ convert it to exponential form. $\bf{\text{Solution Details:}}$ Dividing both sides by $ 5 ,$ the equation above is equivalent to \begin{array}{l}\require{cancel} \ln x=\dfrac{9}{3} \\\\ \ln x=3 .\end{array} Since $\ln x=\log_e x,$ the equation above is equivalent to \begin{array}{l}\require{cancel} \log_e x=3 .\end{array} Since $y=b^x$ is equivalent to $\log_b y=x,$ the exponential form of the equation above is \begin{array}{l}\require{cancel} e^3=x \\\\ x=e^3 .\end{array}
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