College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises: 71

Answer

$\log_2a+\log_2b-\log_2c-\log_2d$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of radicals and the properties of logarithms to rewrite the given expression, $ \log_2\dfrac{ab}{cd} .$ $\bf{\text{Solution Details:}}$ Using the Quotient Rule of Logarithms, which is given by $\log_b \dfrac{x}{y}=\log_bx-\log_by,$ the expression above is equivalent \begin{array}{l}\require{cancel} \log_2(ab)-\log_2(cd) .\end{array} Using the Product Rule of Logarithms, which is given by $\log_b (xy)=\log_bx+\log_by,$ the expression above is equivalent \begin{array}{l}\require{cancel} \log_2(ab)-(\log_2c+\log_2d) \\\\= \log_2(ab)-\log_2c-\log_2d \\\\= \log_2a+\log_2b-\log_2c-\log_2d .\end{array}
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