AMC 12 2007b Problem 17

If $a$ is a nonzero integer and $b$ is a positive number such that $ab^2=\log_{10}b$, what is the median of the set $\{0,1,a,b,1/b\}$?

$\mathrm {(A)} 0 \mathrm {(B)} 1 \mathrm {(C)} a \mathrm {(D)} b \mathrm {(E)} \frac{1}{b}$