Using logarithmic rules, we can simplify the expression as follows:
log 25 + log 2 × log 50 + (log 2)^2 = log (25 × 2^(log 50) × 2^(log 2^2)) [using log(a) + log(b) = log(ab) and log(a^b) = b log(a)] = log (25 × 2^(log 50) × 2^(2 log 2)) [simplifying 2^(log 2^2) to 2^(2 log 2)] = log (25 × 2^(log 50) × 4) [simplifying 2^(2 log 2) to 4] = log (25 × 100 × 4) [simplifying 2^(log 50) to 100] = log 25,000
Therefore, the simplified expression is log 25,000.
