证明m∧logaN=n∧logaM.

问题描述:

证明m∧logaN=n∧logaM.

令x=M^logaN
则取以a为底的对数
loga(x)
=loga[M^logaN]
=logaN*logaM
=logaM*logaN
=loga[N^logaM]
所以x=N^logaM
所以M^logaN=N^logaM