1. **State the problem:** Simplify the expression given by $\log y = 3\log x + \log 3 - \log 6$. 2. **Recall logarithm rules:** - $\log a + \log b = \log(ab)$ - $\log a - \log b = \log\left(\frac{a}{b}\right)$ - $n \log a = \log(a^n)$ 3. **Apply the power rule:** $$\log y = \log(x^3) + \log 3 - \log 6$$ 4. **Combine the addition terms:** $$\log y = \log(3x^3) - \log 6$$ 5. **Apply the subtraction rule:** $$\log y = \log\left(\frac{3x^3}{6}\right)$$ 6. **Simplify the fraction:** $$\frac{3x^3}{6} = \frac{x^3}{2}$$ 7. **Final simplified form:** $$\log y = \log\left(\frac{x^3}{2}\right)$$ 8. **Since logarithm is one-to-one, equate arguments:** $$y = \frac{x^3}{2}$$ **Answer:** $y = \frac{x^3}{2}$