Let \(P = \log_a b,\) where
\(P = \log_2 3 \cdot \log_3 4 \cdot \log_4 5 \cdots \log_{2008} 2009\)
and a and b are relatively prime positive integers. Find the smallest possible value of a+b.
$P = \log_3 1004$, so $a + b = 3 + 1004 = 1007$.
+79 
