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: 34

Answer

$x=-4$

Work Step by Step

We are given the equation $3^{x}=\frac{1}{81}$. First, we must write both sides using the same base. $3^{x}=3^{-4}=\frac{1}{81}$ Next, we must take the natural log of both sides. $ln(3^{x})=ln(3^{-4})$ $xln(3)=-4ln(3)$ Divide both sides by $ln(3)$. $x=-4$
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