[（1-log63）^2+log62*log618]/log64这里面的平方怎么去化,最要的是过程.

Question

[（1-log6 3）^2+log6 2 *log6 18]/log6 4
这里面的平方怎么去化,最要的是过程.

Answer 1

(log 6 2)(log6 18) = (log 6 2)·(log6 2 + log6 9)
= (log 6 2)·(log6 2 + 2log6 3)
= (log6 2)^2 + 2(log6 2)·(log6 3)
(1 - log6 3)^2 = (log6 3)^2 - 2log6 3 + 1
∴分子 = (log6 3 + log6 2)^2 + 1 - 2log6 3
= 2 - 2log6 3 = 2log6 2
而log6 4 = 2log6 2
∴原式 = 1