Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set - Page 810: 56

$\log_a \dfrac{2x^4}{y^3}$

Using the properties of logarithms, the given expression, $ \log_a 2x+3(\log_ax-\log_ay) ,$ simplifies to \begin{array}{l}\require{cancel} \log_a 2x+3\log_ax-3\log_ay \\\\= \log_a 2x+\log_ax^3-\log_ay^3 \\\\= \log_a \dfrac{2x\cdot x^3}{y^3} \\\\= \log_a \dfrac{2x^4}{y^3} .\end{array}