College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.4: 5

Answer

$x=3$

Work Step by Step

We are given the exponential equation $2^{2x-1}=32$. We can express each side using a common base and then solve for $x$. $2^{2x-1}=2^{5}=32$ Take the natural log of both sides. $ln(2^{2x-1})=ln(2^{5})$ $(2x-1)ln(2)=5ln(2)$ Divide both sides by $ln(2)$. $2x-1=5$ Add 1 to both sides. $2x=6$ Divide both sides by 2. $x=3$
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