2008 AMC12 A #16

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

(A) \(40\)          (B) \(56\)         (C) \(76\)          (D) \(112\)          (E) \(143\)

정답 (D)