College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.2: 103

Answer

$x=\frac{1}{64}$

Work Step by Step

From the definition of the logarithmic function on page 456, we know that $y=log_{b}x$ is equivalent to $b^{y}=x$ (for $x\gt0$, $b\gt0$, and $b\ne1$). Therefore, $log_{4}x=-3$ is equivalent to $4^{-3}=x$ in logarithmic form. We know that $4^{-3}=\frac{1}{4^{3}}=\frac{1}{64}$, so $x=\frac{1}{64}$.
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