a2a4a6a8a10=(a6)^5=(a1•q^5)^5=a1^5•2^25,
f(a2a4a6a8a10)=25,
即log2(a1^5•2^25) =25,
所以a1^5•2^25=2^25,a1=1.
∴an=2^(n-1).
f(a1)+f(a2)+……+f(a2009)= log2(a1)+ log2(a2)+ ……+ log2(a2009)
= log2(a1 a2……a2009)
= log2(1•2•2^2•……•2^2008)
=1+2+3+……+2008=1004×2009=2017036.
所以2^[f(a1)+f(a2)+~+f(a2009)]= 2^2017036.