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: 36

Answer

$\dfrac{3}{4}$

Work Step by Step

Using $\log_bx^m=m\log_bx$ or the Power Rule of Logarithms, the given expression, $ \log_{16}8 ,$ is equivalent to \begin{array}{l}\require{cancel} \log_{16}\left(\sqrt[4]{16}\right)^3 \\\\= \log_{16}16^{3/4} \\\\= \dfrac{3}{4}\log_{16}16 .\end{array} Since $\log_bb=1,$ the expression, $ \log_{16}16 ,$ simplifies to $1$. \begin{array}{l}\require{cancel} \dfrac{3}{4}(1) \\\\= \dfrac{3}{4} .\end{array}
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