Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set - Page 810: 53

$\log_a x$

Using the properties of logarithms, the given expression, $ \log_a x^2-2\log_a \sqrt{x} ,$ is equivalent to \begin{array}{l}\require{cancel} \log_a x^2-\log_a \left( \sqrt{x} \right)^2 \\\\= \log_a x^2-\log_a x \\\\= \log_a \dfrac{x^2}{x} \\\\= \log_a x .\end{array}