已知m,n均为正数,且2^m=3^n,求证m/n=log2(底)3(真)

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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=log

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)