Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 9 - Section 9.3 - Logarithmic Functions - 9.3 Exercises - Page 606: 38

Answer

-2.8074

Work Step by Step

For all positive numbers $a$, where $a\ne1$, and all positive numbers $x$, we know that $y=log_{a}x$ means the same as $x=a^{y}$. Therefore, $log_{2}(\frac{1}{7})=x$ means the same as $2^{x}=\frac{1}{7}$. By using a calculator to approximate, we know that $x=-2.8074$, because $2^{-2.8074}=\frac{1}{7}$.
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