(log2 6)×(log3 6)-(log2 3+log3 2)=

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(log26)×(log36)-(log23+log32)=(log26)×(log36)-(log23+log32)=(log26)×(log36)-(log23+log32)=log26=log2

(log2 6)×(log3 6)-(log2 3+log3 2)=
(log2 6)×(log3 6)-(log2 3+log3 2)=

(log2 6)×(log3 6)-(log2 3+log3 2)=
log2 6=log 2 2+log 2 3=1+log 2 3,
log3 6=log 3 2+log3 3=1+log 3 2
log2 3=ln3/ln2,log3 2=ln2/ln3
所以
(log2 6)×(log3 6)-(log2 3+log3 2)
=(1+log2 3)*(1+log 3 2)-(log2 3+log3 2)
=1+log2 3*log3 2
=1+1=2