Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set - Page 810: 55

$\log_a \dfrac{y^5\sqrt{x}}{x^2}$

Using the properties of logarithms, the given expression, $ \dfrac{1}{2}\log_a x+5\log_a y-2\log_a x ,$ simplifies to \begin{array}{l}\require{cancel} \log_a x^{1/2}+\log_a y^5-\log_a x^2 \\\\= \log_a \sqrt{x}+\log_a y^5-\log_a x^2 \\\\= \log_a \dfrac{y^5\sqrt{x}}{x^2} .\end{array}