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: 37

Answer

$x=\dfrac{e^{1.5}}{4}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ \ln(4x)=1.5 ,$ convert it to exponential form. $\bf{\text{Solution Details:}}$ Since $\ln x=\log_e x,$ the equation above is equivalent to \begin{array}{l}\require{cancel} \log_e(4x)=1.5 .\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^{1.5}=4x \\\\ 4x=e^{1.5} \\\\ x=\dfrac{e^{1.5}}{4} .\end{array}
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