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: 85

Answer

$0.7781$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Laws of Logarithms to find an equivalent expression for the given expression, $ \log_{10} 6 .$ Then substitute the given logarithmic values, $\log_{10} 2= 0.3010 $ and $\log_{10} 3= 0.4771 ,$ as necessary. $\bf{\text{Solution Details:}}$ Using the Product Rule of Logarithms, which is given by $\log_b (xy)=\log_bx+\log_by,$ the given expression is equivalent \begin{array}{l}\require{cancel} \log_{10} (2\cdot3) \\\\= \log_{10} 2+\log_{10} 3 .\end{array} Substituting the known values of the logarithmic expressions results to \begin{array}{l}\require{cancel} 0.3010+0.4771 \\\\= 0.7781 .\end{array}
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