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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.

 Apr 18, 2021
 #1
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$P = \log_3 1004$, so $a + b = 3 + 1004 = 1007$.

 May 2, 2021

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