y=lg(x/3)×lg(x/12)=(lgx-lg3)(lgx-lg12)=(lgx)^2-(lg3+lg12)lgx+lg3lg12=(lgx)^2-2lg6lgx+lg3lg12=(lgx-lg6)^2+lg3lg12-(lg6)^2=(lgx-lg6)^2-(lg2)^2故当x=6时有最小值-(lg2)^2.