(log6 3)^2+log6 18乘以log6 2急求!!!!!!!!!!!!!!

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(log6 3)^2+log6 18乘以log6 2急求!!!!!!!!!!!!!!
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(log6 3)^2+log6 18乘以log6 2急求!!!!!!!!!!!!!!
(log6 3)^2+log6 18乘以log6 2
急求!!!!!!!!!!!!!!

(log6 3)^2+log6 18乘以log6 2急求!!!!!!!!!!!!!!
[log6(3)]²+log6(18)×log6(2)
=[log6(3)]²+[log6(3)+log6(6)]log6(2)
=[log6(3)]²+log6(3)×log6(2)+log6(6)×log6(2)
=[log6(3)]²+log6(3)×log6(2)+log6(2)
=log6(3)[log6(3)+log6(2)]+log6(2)
=log6(3)log6(6)+log6(2)
=log6(3)+log6(2)
=log6(6)
=1

log6 3=log6 (6/2)=log6 6-log6 2=1-log6 2 则log6 2=1-log6 3
log6 18×log6 2=log6 (6×3)×(1-log6 3)=(1+log6 3)×(1-log6 3)=1-(log6 3)²
所以原式=(log6 3)²+1-(log6 3)²=1