Question

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 $a+b.$

Answer 1

2011. Y No1 ever answer my question :( lewl