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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.

 Jun 1, 2020
 #1
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This:  logn(2, 3)* logn(3, 4)* logn(4, 5) *logn(5, 6)*logn(6, 7)*logn(7, 8)*logn(8,9)*logn(9,10*.......*log(2008, 2009) is equivalent to: log(2009) / log(2).

 

So, a = 2  and   b=2009

 Jun 1, 2020
 #2
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thank you! :))

Guest Jun 1, 2020

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