log(a^n)M=1/nlog(a)(M) 怎么证明?

用换底公式证明.
证：设c>0,且c≠1,则：
log(a^n)M=log(c)M /log(c)(a^n)=log(c)M /[n*log(c)a]=1/n*[log(c)M/log(c)a]=1/nlog(a)M
所以命题得证.

设左式等于数k,则
(a^n)^k=M,
a^(nk)=M.
则有nk=log(a)(M)
k=1/nlog(a)(M)
即左式=右式