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

$\dfrac{3}{2}$
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}