已知m,n均为正数,且2^m=3^n,求证m/n=log2(底)3(真)

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/09 17:33:29
已知m,n均为正数,且2^m=3^n,求证m/n=log2(底)3(真)

已知m,n均为正数,且2^m=3^n,求证m/n=log2(底)3(真)
已知m,n均为正数,且2^m=3^n,求证m/n=log2(底)3(真)

已知m,n均为正数,且2^m=3^n,求证m/n=log2(底)3(真)
m,n均为正数,且2^m=3^n
设2^m=3^n=a>0
m=log2(a)
n=log3(a)
m/n
=log2(a)/log3(a)
=log2(a)*loga(3).用换底公式loga(3)*log3(a)=1
=log2(3)