求对数函数公式的推导log(a)(M^n)=nlog(a)(M) 和log(a)(N)=log(b)(N) / log(b)(a)_数学解答

求对数函数公式的推导
log(a)(M^n)=nlog(a)(M)
和log(a)(N)=log(b)(N) / log(b)(a) 的推导

人气：451 ℃　时间：2020-02-06 10:02:13

解答

log(a)(M^n)
=log(a)(M*M*M*..M)(n个M)
=log(a)（M）+log(a)（M）+log(a)（M）+.+log(a)（M）（n个log(a)（M））
=nlog(a)(M)
log(a)(N)
=log(a)[b^log(b)(N)]
=log(b)(N) log(a)(b)
=log(b)(N) log(a)(a^log(b)(a))
=log(b)(N) / log(b)(a)