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: 57


$\log_a (x-3)$

Work Step by Step

Using the properties of logarithms, the given expression, $ \log_a (x^2-9)-\log_a (x+3) ,$ simplifies to \begin{array}{l}\require{cancel} \log_a \dfrac{x^2-9}{x+3} \\\\= \log_a \dfrac{(x+3)(x-3)}{x+3} \\\\= \log_a \dfrac{(\cancel{x+3})(x-3)}{\cancel{x+3}} \\\\= \log_a (x-3) .\end{array}
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