Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.3 One-to-One Functions; Inverse Functions - 5.3 Assess Your Understanding - Page 282: 78

Answer

$\{-1,-\frac{1}{3}\}$.

Work Step by Step

As $9=3^2,\ 27=3^3$, we have $3^{4x}\cdot 3^{3x^2}=3^{-1}$. Thus we have $3x^2+4x=-1$ or $3x^2+4x+1=0$, which gives $x=-1,-\frac{1}{3}$ or $\{-1,-\frac{1}{3}\}$. Checking answers, they are both good.
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