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: 76

Answer

$\log_b\dfrac{km}{a}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Laws of Logarithms to write the given expression, $ \log_bk+\log_bm-\log_ba ,$ as a single logarithm. $\bf{\text{Solution Details:}}$ 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_b(km)-\log_ba .\end{array} 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_b\dfrac{km}{a} .\end{array}
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