(log6 3)^2+【(log6 18)/(log2 6)]
= (lg3/lg6)^2+[(lg18/lg6)/(lg6/lg2)]
= (lg3/lg6)^2+(lg18/lg6)*(lg2/lg6)
= (lg3/lg6)^2+(lg18*lg2/lg6*lg6)
= (lg3/lg6)^2+[lg(9*2)*lg2/lg6*lg6)]
= (lg3/lg6)^2+[(2lg3+lg2)*lg2/lg6*lg6)]
= (lg3)^2/(lg6)^2+[2lg3*lg2+(lg2)^2]/(lg6)^2
= [(lg3)^2+2lg3*lg2+(lg2)^2]/(lg6)^2
= (lg3+lg2)^2/(lg6)^2
=[ lg(3*2)]^2/(lg6)^2
= (lg6)^2/(lg6)^2
=1