Let's solve the equation 10x = 0.2 for x step by step:

1. Taking the logarithm of both sides, we get: \(\log 10x = \log 0.2\)
2. Using the logarithm product rule, we get: \(x \log 10 = \log 0.2\)
3. Since the logarithm of 10 to the base 10 is 1, we get: \(x = \log 0.2\)
4. Using the logarithm quotient rule, we get: \(x = \log \frac{1}{5}\)
5. Using the logarithm power rule, we get: \(x = -\log 5\)
6. Since \(\log 5 = \log (10 \div 2) = \log 10 - \log 2 = 1 - 0.3010 = 0.6990\), we get: \(x = -0.6990\)