Question

方程lgx+lgx^3+lgx^5+...+lgx^2n-1=2n^2的解为多少?

Answer 1

lgx+lgx^3+lgx^5+...+lgx^2n-1=lgx^(1+3+...+2n-1)=lgx^(n^2)=n^2*lgx=2n^2,所以lgx=2,x=100.