1. The problem is to find the value of $\log (0.25 \times 0.025)$.\n\n2. First, multiply the numbers inside the logarithm: $$0.25 \times 0.025 = 0.00625.$$\n\n3. So the problem reduces to finding $$\log 0.00625.$$\n\n4. Express $0.00625$ as a fraction or power of 10: $$0.00625 = \frac{625}{100000} = \frac{5^4}{10^5} = \frac{625}{100000}.$$\n\n5. Using logarithm properties: $$\log 0.00625 = \log \left(\frac{5^4}{10^5}\right) = \log 5^4 - \log 10^5 = 4 \log 5 - 5.$$\n\n6. Knowing $\log 10 = 1$ and $\log 5 \approx 0.69897$, calculate: $$4 \times 0.69897 - 5 = 2.79588 - 5 = -2.20412.$$\n\n7. Therefore, $$\log (0.25 \times 0.025) = \log 0.00625 \approx -2.204.$$