Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Section 9.5 - Logarithmic Functions - Exercise Set: 52

Answer

$x=-4$

Work Step by Step

If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x$ and every real number $y$. Therefore, $log_{3}\frac{1}{81}=x$ is equivalent to $3^{x}=\frac{1}{81}$. We know that $x=-4$, because $3^{-4}=\frac{1}{3^{4}}=\frac{1}{81}$.
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