1. **State the problem:** Simplify the expression $3 \log_3 5 + \log_3 6$. 2. **Recall the logarithm rules:** - $a \log_b c = \log_b c^a$ (power rule) - $\log_b x + \log_b y = \log_b (xy)$ (product rule) 3. **Apply the power rule:** $$3 \log_3 5 = \log_3 5^3 = \log_3 125$$ 4. **Rewrite the expression:** $$\log_3 125 + \log_3 6$$ 5. **Apply the product rule:** $$\log_3 (125 \times 6) = \log_3 750$$ 6. **Final answer:** $$\boxed{\log_3 750}$$