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 \(a+b.\)
The product is 11.97226185..., or $\log_2 4018$. So a + b = 2 + 4018 = 4020.
P ==10.97226185
10.97226185 = Log_a(b)
b =a^10.97226185
a ==2 and b==2009
+75 
