AMC 12 2003b Problem 17

If $\log (xy^3) = 1$ and $\log (x^2y) = 1$, what is $\log (xy)$?

$\mathrm{(A)}\ -\frac 12 \mathrm{(B)}\ 0 \mathrm{(C)}\ \frac 12 \mathrm{(D)}\ \frac 35 \mathrm{(E)}\ 1$