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)M2.log(a)M^(m/n)=(m/n)log(a)M,log(a)M^(-m/n)=(-m/n)log(a)M3.log(a^n)M^n=log(a)M,log(a^n)M^m=(m/n)log(a)M4.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)M5.log(a)b×log(b)c×log(c)a=1