颜渊论御马讲了什么道理

求学站 人气:3.33W

对数的运算性质

颜渊论御马讲了什么道理

当a>0且a≠1时,M>0,N>0,那么:

(1)log(a)(MN)=log(a)(M)+log(a)(N);

(2)log(a)(M/N)=log(a)(M)-log(a)(N);

(3)log(a)(M^n)=nlog(a)(M) (n∈R)

(6)换底公式:log(A)M=log(b)M/log(b)A (b>0且b≠1)

设a=n^x则a^(log(b)n)=(n^x)^log(b)n=n^(x·log(b)n)=n^log(b)(n^x)=n^(log(b)a)

log(a)a^b=b 证明:设a^log(a)N=X,log(a)N=log(a)X,N=X