How do you write Log 100 = 2 in exponential form?

If there is no base number attached to $\log$ then you may assume it is $10 , \mathmr{and} \log X = {\log}_{10} X$
${\log}_{10} 100 = 2$
Which means that if you raise $10$ to the power of $2$, you will get $100$, or:
${\log}_{10} 100 = 2 \to {\log}_{10} {10}^{2} = 2 \to {10}^{2} = 100$