Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.8 - Exponential and Logarithmic Equations and Problem Solving - Exercise Set: 9

Answer

$x=3+\dfrac{\log5}{\log2}\approx5.3219$

Work Step by Step

$2^{x-3}=5$ Apply $\log$ to both sides of the equation: $\log2^{x-3}=\log5$ Take $x-3$ down to multiply in front of its respective $\log$: $(x-3)\log2=\log5$ Solve for $x$: $x-3=\dfrac{\log5}{\log2}$ $x=3+\dfrac{\log5}{\log2}\approx5.3219$
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