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 - Page 597: 38



Work Step by Step

We are given the equation $(\frac{4}{3})^{x}=\frac{27}{64}$. First, we must write both sides using the same base. $(\frac{4}{3})^{x}=(\frac{4}{3})^{-3}=\frac{27}{64}$ Note that $(\frac{4}{3})^{-3}=\frac{1}{(\frac{4}{3})^{3}}=\frac{1}{\frac{64}{27}}=\frac{27}{64}$. Next, we must take the natural log of both sides. $ln((\frac{4}{3})^{x})=ln((\frac{4}{3})^{-3})$ $xln(\frac{4}{3})=-3ln(\frac{4}{3})$ Divide both sides by $ln(\frac{4}{3})$. $x=-3$
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