log6 2*log6 18+log6 81/4log3 6

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log62*log618+log681/4log36log62*log618+log681/4log36log62*log618+log681/4log36=log62×(1+log63)+log63

log6 2*log6 18+log6 81/4log3 6
log6 2*log6 18+log6 81/4log3 6

log6 2*log6 18+log6 81/4log3 6
=log6 2×(1+log6 3)+log6 3/log3 6
=(1-log6 3)(1+log6 3)+log²6 3
=1-log²6 3+log²6 3
=1

中间的一些过程
log6 2=log6 6/3=log6 6-log6 3=1-log3
log6 18=log6 3+log6 6=1+log6 3
log6 81=log6 3^4=4log6 3
1/log3 6=log6 3

log6 2*log6 18+log6 81/4log3 6
=log6 2*(log6 9+log6 2)+log6 3/log636
=(log6 2)^2+2log6 2*log6 3+(log6 3)^2
=(log6 2+log3 6)^2
=[log6 (2*3)]^2
=1