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 - 12.3 Logarithmic Functions - 12.3 Exercise Set: 20



Work Step by Step

Using $\log_bx^m=m\log_bx$ or the Power Rule of Logarithms, the given expression, $ \log_{8}\dfrac{1}{64} ,$ is equivalent to \begin{array}{l}\require{cancel} \log_{8}64^{-1} \\\\= \log_{8}(8^2)^{-1} \\\\= \log_{8}8^{2(-1)} \\\\= \log_{8}8^{-2} \\\\= -2\log_{8}8 .\end{array} Since the $\log_bb=1,$ the expression, $ -2\log_{8}8 ,$ simplifies to \begin{array}{l}\require{cancel} -2(1) \\\\= -2 .\end{array}
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