數(shù)學(xué)中l(wèi)og的基本知識 關(guān)于log的常用公式?
關(guān)于log的常用公式?(1)Loga(m.n)=longam longan(2)longa(m/n)=longam longan(3)logam的n次方=nlogam(4)logam的n次方=loga
關(guān)于log的常用公式?
(1)Loga(m.n)=longam longan
(2)longa(m/n)=longam longan
(3)logam的n次方=nlogam
(4)logam的n次方=logam的n次方,或=1/nlogam
(5)Loga m的n次方,=1/nlogam
(6)logaa=1
(7)Logan=n(A>0和A不等于1,n>0)
(8)logab=logmb/logma(底部公式)
PS
LG10=LG(公共對數(shù))
loge=ln(自然對數(shù))
loga1=0
Log(1/a)(1/b)=Log
(a^-1)(b^-1)=-1LOG AB/-1=Log a
(b)Log a(b)*Log b(a)=1LOG e(x)=ln(x)LG(x)=Log 10(x)對數(shù)公式是數(shù)學(xué)中常用的公式。如果a^x=n(a>0,a≠1),則x稱為n的對數(shù),以a為底,表示為x=log(a)(n),其中a寫在log的右下角。其中a為對數(shù)的底,n為真數(shù)
log,計算公式為:x=log(a)(n)。對數(shù)公式是數(shù)學(xué)中常用的公式。如果a^x=n(a>0,a≠1),則x稱為n的對數(shù),以a為底,表示為x=log(a)(n),其中a寫在log的右下角。
有關(guān)log的計算公式?
基本屬性:
1,a^(log(a)(b))=b
2,log(a)(a^b)=b
3,log(a)(MN)=log(a)(m)log(a)(n)
4,log(a)(m△n)=log(a)(m)-log(a)(n)
5,log(a)(m^n)=NLog(a)(m)
6,log(a^n)M=1/NLog(a)(M)底部公式:㏒C B㏒a B=━━━━㏒C B下推公式:log(a^n)(B^M)=M/n*[log(a)(B)
logx計算公式?
答案:如何計算log?
這一切都需要工具:電腦或數(shù)學(xué)手表。
例如,對數(shù)基3,真數(shù)字10=對數(shù)基10,真數(shù)字10/對數(shù)基10,真數(shù)字3=1/Lg3≈1/0.4771≈2.0959
當(dāng)a>0和a≠1時,M>0,n>0,然后:
(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)變底公式:log(a)m=log(b)m/log(b)a(b>0和b≠1)
(5)a ^(log(b)n)=n ^(log(b)a)證明:
設(shè)a=n^x log(log(log(log(log)(log)日志日志(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)(log)M
3。Log(a^n)m^n=Log(a)m,Log(a^n)m^m=(m/n)Log(a)m
4。Log(基于帶n個字根的a)(基于帶n個字根的m)=Log(a)m,
Log(基于帶n個字根的a)(基于帶m個字根的m)=(m/n)Log(a)m
5。Log(a)B×Log(B)C×Log(C)a=1
對數(shù)和指數(shù)的關(guān)系
當(dāng)a>0和a≠1時,a^x=n,x=㏒(a)n
!](1)Log a(m.n)=龍眼(2)龍眼(m/n)=龍眼(3)logam到n次方=nlogam(4)logam到n次方=logam的n次方,or=1/nlogam(5)loga到n次方m,=1/nlogam(6)logaa=1(7)Logan=n(A>0,A不等于1,n>0)(8)logab=logmb/logma(下式)pslg10=LG(公對數(shù))loge=ln(自然對數(shù))loga1=0