0且a?l)对n=log(a)(b)基本性对,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)" />
大学高数公式大全
对的性对及推对数
用’表示乘方?用log (a) (b)表示以a对底?b的对数
*表示乘?号/表示除号
定对式,
若a"n=b(a>0 且a?l)
对n=log(a)(b)
基本性对,
1. a" (log (a) (b)) =b
2. 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)
推对
1?对就不用推了?直接山定对式可得个吧(把定对式中的[n=log(a) (b)]对入a n=b) 2?
MN=M*N
山基本性对1(对掉M和N)
a"[log(a)(MN)] = a"[log(a)(M)] * a"[log(a)(N)]
山指的性对数
a"[log(a)(MN)] = a"{[log(a)(M)] + [log(a)(N)]}
乂因对指函是对对函?所以数数数
log (a) (MN) = log (a) (M) + log (a) (N) 3?与2 对似对理
MN=M/N
山基本性对1(对掉M和N)
a"[log(a)(M/N)] = a"[log(a)(M)] / a"[log(a)(N)]
山指的性对数
a"[log(a)(M/N)] = a"{[log(a)(M)] - [log(a) (N)]}
乂因对指函是对对函?所以数数数
log (a) (M/N) = log (a) (M) - log (a) (N) M n=M n
山基本性对1(对掉M ) a"Elog(a)(M"n)] = {a"[log(a)(M)]}"n
log (a) (M"n) =nlog(a) (M)
其他性对,
性对一,对底公式
log (a) (N)=log(b) (N) / log(b) (a)推对如下
N = a"[log(a)(N)]
a = b"[log(b) (a)]
对合式可得两
N = {b"[log(b) (a)]} "[log(a) (N)] = b"{[log(a) (N)]*[log(b) (a)]} 乂因对 X=b^[log(b) (X)]
所以
b"[log(b) (N)] = b" {[log(a) (N)]*Elog ⑹(a)]}
所以
log(b) (N) = [log(a) (N)]*Elog(b) (a)] {对步不明口或有疑对看上面的}所
以 log (a) (X) =log (b) (X) / log(b) (a)
性对二,;不知道什对名字,
log(a"n) (b"m) =m/n*[ 1 og (a) (b)]推对如下 4?与2对似对理
山指的性对数
a"Elog(a)(M"n)] = a"{[log(a)(M)]*n} 乂因对指函是对对函?所以数数数
Ill对底公式[Inx是log(e) (x),e称数作自然对的底]
log(a"n) (b"m)=ln(a"n) / ln(b"n)山基本性对4 可得
log(a"n) (b^m) = [n*ln(a)] / [m*ln(b)] = (m/n)*{[ln(a)] / [ln(b)]} 再山对底公式
log(a"n) (b"m)=m/n*[log(a) (b)] ——
—-;性对及推对完,公式三:
log (a) (b)=l/log (b) (a)
对明如下:
山对底公式log (a) (b)=log (b) (b)/log (b) (a) 取以b对底的对数,log(b) (b)=l
=l/log(b)(a)
对可对形得:
log (a) (b)*log(b) (a)=l
三角函的和差化对公式数
sin a ? sin 3,2sin: a , P , /2?cos: a
B,/2
sin a
sin P , 2cos: a , B,/2?sin; a
B,/2
cos a , cos B,2cos: a , B , /2?cos: a B,/2
cos a
cos P ,,2sin; a , B,/2?sin: a B,/2
三角函的对化和差公式数
sin a ?cos B ,1/2 [sin; a , B , , sin: a P ,] cos a ?sin P , 1/2 [sin; a , Psin: a 3 ,]
cos a ?cos P , 1/2 [cos: a , P 八cos: a B,] sin a ?sin 3 , -1/2 [cos; a ,