AMC 12 2003a Problem 24

If $a\geq b > 1,$ what is the largest possible value of $\log_{a}(a/b) + \log_{b}(b/a)?$

$\mathrm{(A)}\ -2 \mathrm{(B)}\ 0 \mathrm{(C)}\ 2 \mathrm{(D)}\ 3 \mathrm{(E)}\ 4$