Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set - Page 810: 40

$4\log_a x-\log_a y-2\log_a z$

Using the properties of logarithms, the given expression, $ \log_a \dfrac{x^4}{yz^2} ,$ is equivalent to \begin{array}{l}\require{cancel} \log_a x^4-\log_a (yz^2) \\\\= \log_a x^4-\left( \log_a y+\log_a z^2 \right) \\\\= \log_a x^4-\log_a y-\log_a z^2 \\\\= 4\log_a x-\log_a y-2\log_a z .\end{array}