AMC 12 2008a Problem 16

The numbers $\log(a^3b^7)$, $\log(a^5b^{12})$, and $\log(a^8b^{15})$ are the first three terms of an arithmetic sequence, and the $12^\text{th}$ term of the sequence is $\log(b^n)$. What is $n$?

$\mathrm{(A)}\ 40 \mathrm{(B)}\ 56 \mathrm{(C)}\ 76 \mathrm{(D)}\ 112 \mathrm{(E)}\ 143$