换底公式an=log_(n+1)^(n+2)=lg(n+2)/lg(n+1),
==>a1*a2*...*ak=lg(k+2)/lg(2)=log_(2) ^(k+2),
依题意,即求当k在[1,2010]内,使得log_(2) ^(k+2)=j为整数,
亦即求当k在[1,2010]内,j为整数,使得2^j=k+2的k.
故可取j=2,3,……,10时的 k=2^j-2.