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 - Page 489: 6



Work Step by Step

We are given the exponential equation $3^{2x+1}=27$. We can express each side using a common base and then solve for $x$. $3^{2x+1}=3^{3}=27$ Take the natural log of both sides. $ln(3^{2x+1})=ln(3^{3})$ $(2x+1)ln(3)=3ln(3)$ Divide both sides by $ln(3)$. $2x+1=3$ Subtract 1 from both sides. $2x=2$ Divide both sides by 2. $x=1$
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