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 - Mid-Chapter Review - Mixed Review - Page 812: 18


$ \displaystyle \log\frac{a}{b^{2}c}$

Work Step by Step

... Group the negative terms (factor out -1) $...=\log a-(2\log b+\log c)\quad$... Apply the property $\log_{a}M^{p}=p\cdot\log_{a}M$ $=\log a-(\log b^{2}+\log c)\quad$... Apply the property $\log_{a}(MN)=\log_{a}M+\log_{a}N$ $=\log a-\log(b^{2}c)\quad$... Apply the property $\displaystyle \log_{a}\frac{M}{N}=\log_{a}M-\log_{a}N$ $=\displaystyle \log\frac{a}{b^{2}c}$
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