Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 9 - Section 9.2 - Exponential Functions - 9.2 Exercises: 37

Answer

$x=-3$

Work Step by Step

We are given the equation $(\frac{3}{2})^{x}=\frac{8}{27}$. First, we must write both sides using the same base. $(\frac{3}{2})^{x}=(\frac{3}{2})^{-3}=\frac{8}{27}$ Note that $(\frac{3}{2})^{-3}=\frac{1}{(\frac{3}{2})^{3}}=\frac{1}{\frac{27}{8}}=\frac{8}{27}$. Next, we must take the natural log of both sides. $ln((\frac{3}{2})^{x})=ln((\frac{3}{2})^{-3})$ $xln(\frac{3}{2})=-3ln(\frac{3}{2})$ Divide both sides by $ln(\frac{3}{2})$. $x=-3$
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