zxm690307
幼苗
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英语名词:logarithms.如果a^b=n,那么log(a)(n)=b.其中,a叫做“底数”,n叫做“真数”,b叫做“以a为底的n的对数”.
log(a)(n)函数叫做对数函数.对数函数中n的定义域是n>0,零和负数没有对数;a的定义域是a>0且a≠1.定义若a^n=b(a>0且a≠1) 则n=log(a)(b)基本性质1、a^(log(a)(b))=b2、log(a)(MN)=log(a)(M)+log(a)(N);3、log(a)(M÷N)=log(a)(M)-log(a)(N);4、log(a)(M^n)=nlog(a)(M)5、log(a^n)(M)=1/nlog(a)(M)推导1、因为n=log(a)(b),代入则a^n=b,即a^(log(a)(b))=b.2、令log(a)(MN)=b,则有a^b=MN;令log(a)(M)=c,log(a)(N)=d,则有a^c=M,a^d=N;(a^c)*(a^d)=a^(c+d)=MN=a^b;则c+d=b;推出log(a)(M)+log(a)(N)=log(a)(MN).3、令log(a)(M÷N)=b,则有a^b=M÷N;令log(a)(M)=c,log(a)(N)=d,则有a^c=M,a^d=N;(a^c)÷(a^d)=a^(c-d)=M÷N=a^b;则c-d=b;推出log(a)(M)-log(a)(N) =log(a)(M÷N).4、令log(a)(M^n)=b,则有a^b=M^n; 令log(a)(M)=c,则有a^c=M;a^b=M^n=(a^c)^n=a^(cn)b=cn;log(a)(M^n)=nlog(a)(M).5、令log(a^n)(M)=b,则(a^n)^b=M,a^(nb)=M;令log(a)(M)=c,则a^c=M;a^c=M=a^(nb),则c=nb;log(a)(M)=nlog(a^n)(M);log(a^n)(M)=1/nlog(a)(M).ln就是指log以e为底的对数,b=ln(a)表示e的b次方等于a.
e=2.71828……,
1年前
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