1. The problem asks to rewrite the expression $$\log_5 \left( \frac{x^4}{y} \right)$$ as a sum or difference of multiples of logarithms. 2. We use the logarithm properties: - $$\log_b \left( \frac{A}{B} \right) = \log_b A - \log_b B$$ (logarithm of a quotient) - $$\log_b (A^n) = n \log_b A$$ (logarithm of a power) 3. Apply the quotient rule: $$\log_5 \left( \frac{x^4}{y} \right) = \log_5 (x^4) - \log_5 (y)$$ 4. Apply the power rule to $$\log_5 (x^4)$$: $$\log_5 (x^4) = 4 \log_5 (x)$$ 5. Substitute back: $$\log_5 \left( \frac{x^4}{y} \right) = 4 \log_5 (x) - \log_5 (y)$$ This is the expression as a sum and difference of multiples of logarithms, with no exponents on variables. Final answer: $$\boxed{4 \log_5 (x) - \log_5 (y)}$$