Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set: 63

Answer

$-1.161$

Work Step by Step

Using the properties of logarithms, the given expression, $ \log_b \dfrac{1}{5} ,$ is equivalent to \begin{array}{l}\require{cancel} \log_b 1-\log_b 5 .\end{array} Since it is given that $\log_b 5=1.161 $ and that the logarithm of $1$ to any defined base is $0$, the expression above, $ \log_b 1-\log_b 5 $, evaluates to \begin{array}{l}\require{cancel} 0-1.161 \\\\= -1.161 .\end{array}
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