Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set - Page 810: 50

$\log_b \left(m^2\sqrt{n} \right)$

Using the properties of logarithms, the given expression, $ 2\log_b m+\dfrac{1}{2}\log_b n ,$ is equivalent to \begin{array}{l}\require{cancel} \log_b m^2+\log_b n^{1/2} \\\\= \log_b m^2+\log_b \sqrt{n} \\\\= \log_b \left(m^2\sqrt{n} \right) .\end{array}