若lg(xy) lg(x 2y)=lg^2 lgx lgy

解: 2 lg(x-2y)=lgx+lgy==>lg(x-2y)^2=lgxy ==>(x-2y)^2=xy ==>x^2-5xy+4y^2=0 ==(x-4y)(x-y)=0 ==>x=4y,or x-y=0 ==>x/y=4 or x/y=1 lg2(x/y)=2 or 0