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: 7

Answer

$x=2$

Work Step by Step

We are given the exponential equation $4^{2x-1}=64$. We can express each side using a common base and then solve for $x$. $4^{2x-1}=4^{3}=64$ Take the natural log of both sides. $ln(4^{2x-1})=ln(4^{3})$ $(2x-1)ln(4)=3ln(4)$ Divide both sides by $ln(4)$. $2x-1=3$ Add 1 to both sides. $2x=4$ Divide both sides by 2. $x=2$
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