从1,2,3,4,7,9中任选2个数作为一个对数的底数与真数,则可得到的对数值个数是多少个?

2025-03-24 01:08:17
推荐回答(2个)
回答1:

首先1不能作为底数、然后2作底数,其他5个数做真数、3作底数,其他作真数、以此类推、可得到25个对数值,再排除相同的答案0就行了,答案是20个对数值

回答2:

总共有A(2,2)×C(6,2)=2×15=30个
(i)其中log1(2)=log1(3)=log1(4)=log1(5)=log1(6)
不存在
去除5个(ii)其中log2(1)=log3(1)=log4(1)=log7(1)=log9(1)都是一样为0
这5个只能算一个
去除4个
(iii)因为log2(4)=log3(9)=2
log4(2)=log9(3)=0.5
再去除2个
(iv)因为log2(3)=log4(9)

log3(2)=log9(4)
再去除2个
则一共有30-5-4-2-2=17个

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