Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set: 68

Answer

$2.745$

Work Step by Step

Using the properties of logarithms, the given expression, $ \log_b 45 ,$ is equivalent to \begin{array}{l}\require{cancel} \log_b (3^2\cdot5) \\\\= \log_b 3^2+\log_b5 \\\\= 2\log_b 3+\log_b5 .\end{array} Since it is given that $\log_b 3=0.792 $ and $\log_b5=1.161$, the expression above, $ 2\log_b 3+\log_b5 ,$ evaluates to \begin{array}{l}\require{cancel} 2(0.792)+1.161 \\\\= 2.745 .\end{array}
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