AHSME 1967 Problem 26

If one uses only the tabular information $10^3=1000$, $10^4=10,000$, $2^{10}=1024$, $2^{11}=2048$, $2^{12}=4096$, $2^{13}=8192$, then the strongest statement one can make for $\log_{10}{2}$ is that it lies between: $\textbf{(A)}\ \frac{3}{10} \text{and} \frac{4}{11} \textbf{(B)}\ \frac{3}{10} \text{and} \frac{4}{12} \textbf{(C)}\ \frac{3}{10} \text{and} \frac{4}{13} \textbf{(D)}\ \frac{3}{10} \text{and} \frac{40}{132} \textbf{(E)}\ \frac{3}{11} \text{and} \frac{40}{132}$