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: 10

Answer

$x=\frac{5}{2}$

Work Step by Step

We are given the exponential equation $4^{x}=32$. We can express each side using a common base and then solve for $x$. $4^{x}=(2^{2})^{x}=2^{2x}$ $32=2^{5}$ $2^{2x}=2^{5}$ Take the natural log of both sides. $ln(2^{2x})=ln(2^{5})$ $2xln(2)=5ln(2)$ Divide both sides by $ln(2)$. $2x=5$ Divide both sides by 2. $x=\frac{5}{2}$
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