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: 60

Answer

$x=\frac{4}{9}$

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, $log_{\frac{2}{3}}x=2$ is equivalent to $(\frac{2}{3})^{2}=x$. $x=\frac{2}{3}\times\frac{2}{3}=\frac{2\times2}{3\times3}=\frac{4}{9}$
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