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

Published by Pearson

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}

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.