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: 24

Answer

$x\approx2.115$

Work Step by Step

Using the properties of equality, the given equation, $ 7.2^x-65=0 ,$ is equivalent to \begin{array}{l}\require{cancel} 7.2^x=65 .\end{array} Taking the natural logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the equation, $ 7.2^x=65 ,$ is \begin{array}{l}\require{cancel} \ln7.2^x=\ln65 \\\\ x\ln7.2=\ln65 \\\\ x=\dfrac{\ln65}{\ln7.2} \\\\ x\approx2.115 .\end{array}
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