﹙log以2为底5的对数+log以4为底125的对数﹚乘以﹙log以3为底2的对数/log以根号3为底的5的对数﹚
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/10/01 09:32:36
﹙log以2为底5的对数+log以4为底125的对数﹚乘以﹙log以3为底2的对数/log以根号3为底的5的对数﹚
为了书写方便,不妨记以a为底b的对数为:log【a】b
(log【2】5+log【4】125)×[(log【3】2)/(log【√3】5)]
=[(lg5)/(lg2)+(lg125)/(lg4)]×{[(lg2)/(lg3)]/[(lg5)/(lg√3)]}
=[(2lg5+lg125)/(2lg2)]×{(lg2)(lg√3)/[(lg3)(lg5)]}
=[(5lg5)/(2lg2)]×{(1/2)(lg2)(lg3)/[(lg3)(lg5)]}
=[(5lg5)/(2lg2)]×(1/2)(lg2)/(lg5)]
=(5/2)×(1/2)
=5
再问: =[(5lg5)/(2lg2)]×(1/2)(lg2)/(lg5)] =(5/2)×(1/2) (1/2)(lg2)/(lg5)为什么直接等于1/2了? 而且 =(5/2)×(1/2) 5? 不等于5啊。。
再答: 不好意思
(log【2】5+log【4】125)×[(log【3】2)/(log【√3】5)]
=[(lg5)/(lg2)+(lg125)/(lg4)]×{[(lg2)/(lg3)]/[(lg5)/(lg√3)]}
=[(2lg5+lg125)/(2lg2)]×{(lg2)(lg√3)/[(lg3)(lg5)]}
=[(5lg5)/(2lg2)]×{(1/2)(lg2)(lg3)/[(lg3)(lg5)]}
=[(5lg5)/(2lg2)]×(1/2)(lg2)/(lg5)]
=(5/2)×(1/2)
=5
再问: =[(5lg5)/(2lg2)]×(1/2)(lg2)/(lg5)] =(5/2)×(1/2) (1/2)(lg2)/(lg5)为什么直接等于1/2了? 而且 =(5/2)×(1/2) 5? 不等于5啊。。
再答: 不好意思
﹙log以2为底5的对数+log以4为底125的对数﹚乘以﹙log以3为底2的对数/log以根号3为底的5的对数﹚
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