f(x)
=lg(100x)*lg(x/10)
=(lg100+lgx)*(lgx-lg10)
=(2+lgx)(lgx-1)
设t=lgx
则f(t)
=(2+t)(t-1)
=t^2+t-1
=(t+1/2)^2-5/4
当t=lgx=-1/2时,f(x)最小值为-5/4