已知:loga1 b1=loga2 b2=……logan bn=N求证:loga1a2……an (b1b2……bn)=N
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/25 08:29:37
![已知:loga1 b1=loga2 b2=……logan bn=N求证:loga1a2……an (b1b2……bn)=N](/uploads/image/z/3878788-4-8.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9Aloga1+b1%3Dloga2+b2%3D%E2%80%A6%E2%80%A6logan+bn%3DN%E6%B1%82%E8%AF%81%3Aloga1a2%E2%80%A6%E2%80%A6an+%EF%BC%88b1b2%E2%80%A6%E2%80%A6bn%EF%BC%89%3DN)
已知:loga1 b1=loga2 b2=……logan bn=N求证:loga1a2……an (b1b2……bn)=N
已知:loga1 b1=loga2 b2=……logan bn=N求证:loga1a2……an (b1b2……bn)=N
已知:loga1 b1=loga2 b2=……logan bn=N求证:loga1a2……an (b1b2……bn)=N
只需做个换底即可
lgb1/lga1=lgb2/lga2=……=lgbn/lgan=N
有分式的合比性质得
(lgb1+lgb2+……+lgbn)/(lga1+lga2+……+lgan)=N
即(lgb1b2……bn)/lg(a1a2……an)=N
然后换底得lga1a2……an(b1b2……bn)=N