1. **State the problem:** Simplify the expression $3 \log 10 + 2 \log 10$. 2. **Recall the logarithm property:** For any logarithm, $a \log b = \log b^a$. 3. **Apply the property:** $$3 \log 10 = \log 10^3 = \log 1000$$ $$2 \log 10 = \log 10^2 = \log 100$$ 4. **Rewrite the expression:** $$3 \log 10 + 2 \log 10 = \log 1000 + \log 100$$ 5. **Use the logarithm addition rule:** $$\log a + \log b = \log (a \times b)$$ 6. **Combine the logs:** $$\log 1000 + \log 100 = \log (1000 \times 100) = \log 100000$$ 7. **Evaluate the logarithm:** Since $\log 10^5 = 5$, and $100000 = 10^5$, we have $$\log 100000 = 5$$ **Final answer:** $5$