2007 AMC 12B 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\qquad \mathrm {(B)} 1\qquad \mathrm {(C)} a\qquad \mathrm {(D)} b\qquad \mathrm {(E)} \frac{1}{b}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.