For a reaction $\mathrm{A} \rightarrow \text{product}$, rate constant is $2 \times 10^{-2}\ \mathrm{s}^{-1}$. The initial concentration of A is $1.0\ \mathrm{mol\ dm}^{-3}$. What is the value of $\log_{10}\!\left(\frac{1}{[\mathrm{A}]_t}\right)$ after 100 seconds?