原式={[log6(6)-log6(3)]²+log6(2)*log6(18)]÷log6(4)
={[log6(6÷3)]²+log6(2)*log6(18)}÷log6(4)
={[log6(2)]²+log6(2)*log6(18)}÷log6(4)
={log6(2)*[log6(2)+log6(18)]}÷log6(4)
=log6(2)*[log6(2×18)]÷log6(4)
=log6(2)*[log6(6²)]÷log6(4)
换底公式
=(lg2/lg6)*2÷(lg4/lg6)
=2lg2÷lg4
=2lg2÷2lg2
=1