1. **State the problem:** Evaluate the expression $$10 \log\left(\frac{10^{78}}{10} + \frac{3 \times 10^{64}}{10} + \frac{6 \times 10^{54}}{10}\right)$$ to 2 significant figures. 2. **Rewrite the expression inside the logarithm:** $$\frac{10^{78}}{10} = 10^{78-1} = 10^{77}$$ $$\frac{3 \times 10^{64}}{10} = 3 \times 10^{64-1} = 3 \times 10^{63}$$ $$\frac{6 \times 10^{54}}{10} = 6 \times 10^{54-1} = 6 \times 10^{53}$$ 3. **Sum the terms inside the logarithm:** $$10^{77} + 3 \times 10^{63} + 6 \times 10^{53}$$ Since $$10^{77}$$ is vastly larger than the other terms, the sum is approximately $$10^{77}$$. 4. **Apply the logarithm:** $$\log(10^{77} + \text{smaller terms}) \approx \log(10^{77}) = 77$$ 5. **Multiply by 10:** $$10 \times 77 = 770$$ 6. **Round to 2 significant figures:** $$770 \to 7.7 \times 10^{2}$$ **Final answer:** $$7.7 \times 10^{2}$$