Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 7 Exponential and Logarithmic Functions - 7.5 Apply Properties of Logarithms - 7.5 Exercises - Skill Practice - Page 511: 65


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Work Step by Step

Let $x=\log_b m\\y=\log_b n$ Rewrite as: $b^x=m\\b^y=n$ Obtain: $\log_b{mn}=\log_b b^xb^y=\log_b b^x b^y=\log_b b^{x+y}=(x+y)\log_b b$ Thus, $x+y=\log_b m+\log_b n\\ \rightarrow \log_b mm=\log_b m+\log_b n$
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