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: 25

Answer

$x\approx0.563$

Work Step by Step

Using the properties of equality, the given equation, $ 19=2e^{4x} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{19}{2}=e^{4x} .\end{array} Taking the natural logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the equation, $ \dfrac{19}{2}=e^{4x} ,$ is \begin{array}{l}\require{cancel} \ln\dfrac{19}{2}=\ln e^{4x} \\\\ \ln\dfrac{19}{2}=4x(\ln e) \\\\ \ln\dfrac{19}{2}=4x(1) \\\\ \ln\dfrac{19}{2}=4x \\\\ \dfrac{\ln\dfrac{19}{2}}{4}=x \\\\ x\approx0.563 .\end{array}
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