Question

已知lgx+lgx^2+...+lgx^10=110,求lgx+(lg^2)x+...+(lg^10)x

Answer 1

lgx+lgx^2+...+lgx^10=110,lg(x*x^2*...*x^10)=110,lgx^55=110,55lgx=110 lgx=2 x=100 lgx+(lg^2)x+...+(lg^10)x =2+2^2+...+2^10 =2^11-2