lgx+lgx^2+lgx^3+……+lgx^n
=lgx+2lgx +3lgx + ...+ nlgx
=(1+2+...n)lgx
=n(n+1)/2 * lgx
所以方程等价于 n(n+1)/2 * lgx = n(n+1)
即1/2 * lgx =1
lgx= 2
x=10^2=100