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 - Page 810: 81


The correction is in red: $\displaystyle \log_{b}\frac{1}{x}=\log_{b}\frac{x}{xx}$ $=\log_{b}x-\color{red}{(\log_{b}x+\log_{b}x)}$ $=-\log_{b}x.$ The mistake is in the improper application of the rule $\displaystyle \log_{a}\frac{M}{N}=\log_{a}M-\log_{a}N$ (the log(denominator) has to be included in parentheses, as the product rule is to be applied on $\log_b(xx)$)

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