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: 9

Answer

$x=\frac{3}{5}$

Work Step by Step

We are given the exponential equation $32^{x}=8$. We can express each side using a common base and then solve for $x$. $32^{x}=(2^{5})^{x}=2^{5x}$ $8=2^{3}$ $2^{5x}=2^{3}$ Take the natural log of both sides. $ln(2^{5x})=ln(2^{3})$ $5xln(2)=3ln(2)$ Divide both sides by $ln(2)$. $5x=3$ Divide both sides by 5. $x=\frac{3}{5}$
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