求对数运算的公式

2个回答

  • 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)   (4)log(a^n)(M)=1/nlog(a)(M)(n∈R)   (5)换底公式:log(A)M=log(b)M/log(b)A (b>0且b≠1)   (6)a^(log(b)n)=n^(log(b)a) 证明:   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)   (7)对数恒等式:a^log(a)N=N;   log(a)a^b=b   (8)由幂的对数的运算性质可得(推导公式)   1.log(a)M^(1/n)=(1/n)log(a)M , log(a)M^(-1/n)=(-1/n)log(a)M   2.log(a)M^(m/n)=(m/n)log(a)M , log(a)M^(-m/n)=(-m/n)log(a)M   3.log(a^n)M^n=log(a)M , log(a^n)M^m=(m/n)log(a)M   4.log(以 n次根号下的a 为底)(以 n次根号下的M 为真数)=log(a)M ,   log(以 n次根号下的a 为底)(以 m次根号下的M 为真数)=(n/m)log(a)M   5.log(a)b×log(b)c×log(c)a=1

    对数与指数之间的关系

    当a>0且a≠1时,a^x=N x=㏒(a)N

    慢慢看吧