Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set - Page 810: 39

$5\log_a x-3\log_a y-\log_a z$

Using the properties of logarithms, the given expression, $ \log_a \dfrac{x^5}{y^3z} ,$ is equivalent to \begin{array}{l}\require{cancel} \log_a x^5-\log_a (y^3z) \\\\= \log_a x^5-\left( \log_a y^3+\log_a z \right) \\\\= \log_a x^5-\log_a y^3-\log_a z \\\\= 5\log_a x-3\log_a y-\log_a z .\end{array}