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: 11

Answer

$x=\frac{3}{2}$

Work Step by Step

We are given the exponential equation $9^{x}=27$. We can express each side using a common base and then solve for $x$. $9^{x}=(3^{2})^{x}=3^{2x}$ $27=3^{3}$ $3^{2x}=3^{3}$ Take the natural log of both sides. $ln(3^{2x})=ln(3^{3})$ $2xln(3)=3ln(3)$ Divide both sides by $ln(3)$. $2x=3$ Divide both sides by 2. $x=\frac{3}{2}$
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