Using the properties of logarithms, specifically $\log(mn) = \log m + \log n$ and $\log(m^n) = n \log m$, we can factor 12 into its prime factors: $12 = 2^2 \times 3$. Therefore, $\log_{10} 12 = \log_{10}(2^2 \times 3) = \log_{10}(2^2) + \log_{10} 3$. Applying the power rule, this becomes $2 \log_{10} 2 + \log_{10} 3$. Substituting the given variables $a$ and $b$, we get $2a + b$. Option 1 represents $\log 6$. Option 3 represents $\log 18$. Option 4 is mathematically incorrect as $\log m^n$ is $n\log m$, not $(\log m)^n$.