## 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 - Page 810: 65

#### Answer

$\dfrac{3}{2}$

#### Work Step by Step

Using the properties of logarithms, the given expression, $\log_b \sqrt{b^3} ,$ is equivalent to \begin{array}{l}\require{cancel} \log_b b^{3/2} \\\\= \dfrac{3}{2}\log_b b .\end{array} Since $\log_b b=1,$ the expression above, $\dfrac{3}{2}\log_b b$, evaluates to \begin{array}{l}\require{cancel} \dfrac{3}{2}(1) \\\\= \dfrac{3}{2} .\end{array}

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