對數(shù)計算公式

性質(zhì)loga(1)=0；②loga(a)=1；③負(fù)數(shù)與零無對數(shù).2對數(shù)恒等式a^logaN=N(a>0 ，a≠1）3運算法則loga(MN)=logaM+logaN；loga(M/N)=logaM－logaN；③對logaM中M的n次方有=nlogaM；如果a=e^m，則m為數(shù)a的自然對數(shù)，即lna=m，e=2.718281828為自然對數(shù)的底。定義： 若a^n=b(a>0且a≠1)則n=log(a)(b)基本性質(zhì)：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)=nl og(a)(M)5、log(a^n)M=1/nl og(a)(M)推導(dǎo)：1、因為n=log(a)(b) ，代入則a^n=b，即a^(log(a)(b))=b 。2、MN=M×N精選范本,供參考！由基本性質(zhì)1(換掉M和N)a^[log(a)(MN)]=a^[log(a)(M)] ×a^[log(a)(N)]由指數(shù)的性質(zhì)a^[log(a)(MN)]=a^{[log(a)(M)]+[log(a)(N)]}又因為指數(shù)函數(shù)是單調(diào)函數(shù)，所以log(a)(MN)=log(a)(M)+log(a)(N)3、與（2）類似處理M/N=M÷N由基本性質(zhì)1(換掉M和N)a^[log(a)(M ÷N)]=a^[log(a)(M)] ÷a^[log(a)(N)]由指數(shù)的性質(zhì)a^[log(a)(M ÷N)]=a^{[log(a)(M)]-[log(a)(N)]}又因為指數(shù)函數(shù)是單調(diào)函數(shù)，所以log(a)(M÷N)=log(a)(M)-log(a)(N)4、與（2）類似處理M^n=M^n由基本性質(zhì)1(換掉M)a^[log(a)(M^n)]={a^[log(a)(M)]}^n由指數(shù)的性質(zhì)a^[log(a)(M^n)]=a^{[log(a)(M)]*n}又因為指數(shù)函數(shù)是單調(diào)函數(shù)，所以log(a)(M^n)=nlog(a)(M)基本性質(zhì)4推廣log(a^n)(b^m)=m/n*[log(a)(b)]精選范本,供參考！[lnxlog(e)(x)e]log(a^n)(b^m)=ln(b^m)÷ln(a^n)e^x=b^m,e^y=a^nlog(a^n)(b^m)=log(e^y)(e^x)=x/y x=ln(b^m),y=ln(a^n)log(a^n)(b^m)=ln(b^m) ÷ln(a^n)4log(a^n)(b^m)=[m×ln(b)]÷[n×ln(a)]=(m÷n)×{[ln(b)]÷[ln(a)]}log(a^n)(b^m)=m ÷n×[log(a)(b)]4b=a^ma=c^nb=(c^n)^m=c^(mn) alog(a)(b)=m .. clog(c)(b)=mn/log(c)(b)/log(a)(b)=n=log(c)(a)log(a)(b)=log(c)(b)/log(c)(a)log(a)(b) a xe alogae=1/ lna5精選范本,供參考！log(1/a)(1/b)=loga(b)loga(b)*logb(a)=16求導(dǎo)數(shù)(xlogax)'=logax+lna其中，logax中的a為底數(shù)，x為真數(shù)；(logax)'=1/xlna特殊的