1. **State the problem:** Evaluate $\log 10^{1000}$. 2. **Recall the logarithm power rule:** $\log a^b = b \log a$. This means we can bring the exponent down as a multiplier. 3. **Apply the rule:** $$\log 10^{1000} = 1000 \log 10$$ 4. **Evaluate $\log 10$:** Since the base is 10, $\log 10 = 1$. 5. **Calculate the final value:** $$1000 \times 1 = 1000$$ 6. **Answer:** $\log 10^{1000} = 1000$.