AHSME 1961 Problem 30

If $\log_{10}2=a$ and $\log_{10}3=b$, then $\log_{5}12=$? $\textbf{(A)}\ \frac{a+b}{a+1} \textbf{(B)}\ \frac{2a+b}{a+1} \textbf{(C)}\ \frac{a+2b}{1+a} \textbf{(D)}\ \frac{2a+b}{1-a} \textbf{(E)}\ \frac{a+2b}{1-a}$