1. State the problem: Express $$\frac{(\log m)^p \sqrt{3 - n}}{m n^2}$$ in terms of $\log m$, $\log n$, and $\log p$. 2. Analyze each part: - Numerator: $(\log m)^p \sqrt{3 - n}$ - Denominator: $m n^2$ 3. Rewrite the denominator using logarithms: $$m n^2 = e^{\log m} e^{2 \log n} = e^{\log m + 2 \log n}$$ 4. Rewrite the entire expression: $$\frac{(\log m)^p \sqrt{3 - n}}{m n^2} = (\log m)^p \sqrt{3 - n} \cdot e^{-\log m - 2 \log n}$$ 5. Express $\sqrt{3 - n}$: Assuming $3 - n > 0$, we keep as is because it cannot be expressed in terms of $\log m$, $\log n$, or $\log p$: $$\sqrt{3 - n} = (3 - n)^{1/2}$$ 6. Final expression: $$\boxed{(\log m)^p \sqrt{3 - n} e^{- \log m - 2 \log n}}$$ Note: $\log p$ does not appear naturally in the expression.