1. **State the problem:** Given the equation $\log y = 3\log + \log 3 - \log 6$, find the value of $y$. 2. **Clarify the expression:** The term $3\log$ is incomplete. Assuming it means $3\log x$ for some base or variable $x$, but since $x$ is not given, we interpret $3\log$ as $3\log 10$ (common logarithm of 10) which equals 3 because $\log 10 = 1$. 3. **Rewrite the equation:** $$\log y = 3 + \log 3 - \log 6$$ 4. **Use logarithm properties:** - $\log a - \log b = \log \frac{a}{b}$ - $\log a + b = \log (10^b \cdot a)$ since $b$ is a number, not a log. 5. **Simplify the right side:** $$\log y = 3 + \log \frac{3}{6} = 3 + \log \frac{1}{2}$$ 6. **Rewrite $3$ as $\log 10^3$:** $$\log y = \log 10^3 + \log \frac{1}{2} = \log \left(10^3 \times \frac{1}{2}\right)$$ 7. **Combine the logs:** $$\log y = \log 500$$ 8. **Conclude:** Since $\log y = \log 500$, then $$y = 500$$ **Final answer:** $y = 500$