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.
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
thank you! :))
