(log3(2)+log9(2))*(log4(3)+log8(3))
答案:2 悬赏:50 手机版
解决时间 2021-11-30 07:28
- 提问者网友：酱爆肉
- 2021-11-30 02:33
(log3(2)+log9(2))*(log4(3)+log8(3))
最佳答案
- 五星知识达人网友：猎心人
- 2021-11-30 04:10
(log3(2) + log9(2)) * (log4(3) + log8(3))
= (lg2/lg3 + lg2/lg9) * (lg3/lg4 + lg3/lg8))
= [lg2/lg3 + lg2/(2lg3)] * [lg3/(2lg2) + lg3/(3lg2)]
= [(2lg2+lg2)/(2lg3)] * [(3lg3+2lg3)/(6lg2)]
= 3lg2/(2lg3)] * 5lg3/(6lg2)
= 3/2 * 5/6
= 5/4
= (lg2/lg3 + lg2/lg9) * (lg3/lg4 + lg3/lg8))
= [lg2/lg3 + lg2/(2lg3)] * [lg3/(2lg2) + lg3/(3lg2)]
= [(2lg2+lg2)/(2lg3)] * [(3lg3+2lg3)/(6lg2)]
= 3lg2/(2lg3)] * 5lg3/(6lg2)
= 3/2 * 5/6
= 5/4
全部回答
- 1楼网友：野味小生
- 2021-11-30 04:45
5/4
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