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: 72

Answer

$\log_2x+\log_2y-\log_2t-\log_2q-\log_2r$

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{xy}{tqr} .$ $\bf{\text{Solution Details:}}$ Using the Quotient Rule of Logarithms, which is given by $\log_b \dfrac{x}{y}=\log_bx-\log_by,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \log_2(xy)-\log_2(tqr) .\end{array} Using the Product Rule of Logarithms, which is given by $\log_b (xy)=\log_bx+\log_by,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \log_2(xy)-(\log_2t+\log_2q+\log_2r) \\\\= \log_2(xy)-\log_2t-\log_2q-\log_2r \\\\= \log_2x+\log_2y-\log_2t-\log_2q-\log_2r .\end{array}
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