高中數(shù)學(xué) 2.2 對(duì)數(shù)函數(shù)知識(shí)表格素材 新人教必修1

axN=㏒aN=x冪指數(shù)冪值冪值真數(shù)底數(shù)1.指數(shù)函數(shù)與對(duì)數(shù)函數(shù)的關(guān)系.對(duì)數(shù)形式特點(diǎn)記法常用對(duì)數(shù)自然對(duì)數(shù)底數(shù)為10底數(shù)為elg

Nln

N2.兩種常用的對(duì)數(shù).3.對(duì)數(shù)的運(yùn)算法則若a＞0，a≠1，M＞0,N＞0運(yùn)算數(shù)學(xué)表達(dá)式自然語(yǔ)言積的對(duì)數(shù)商的對(duì)數(shù)冪的對(duì)數(shù)loga(MN)=logaM+logaNloga(N1?N2?…?Nk)=logaN1+logaN2+…+logaNk（Ni＞0，i=1，2，…，k）正因數(shù)積的對(duì)數(shù)等于同一底數(shù)的各因數(shù)對(duì)數(shù)的和兩個(gè)正數(shù)商的對(duì)數(shù)等于同一底數(shù)的被除數(shù)的對(duì)數(shù)減去除數(shù)的對(duì)數(shù)logaMα=αlogaM(α∈R)正數(shù)冪的對(duì)數(shù)等于冪指數(shù)乘以同一底數(shù)冪的底數(shù)的對(duì)數(shù).4.對(duì)數(shù)函數(shù)的圖象與性質(zhì)底數(shù)圖象定義域值域性質(zhì)a>10<a<1R(0,+∞)(1)過(guò)定點(diǎn)(1，0)，即x=1時(shí)，y=0(3)當(dāng)0<x<1時(shí)，y<0;當(dāng)x>1時(shí)，y>0.(3)當(dāng)x>1時(shí)，y<0.當(dāng)0<x<1時(shí)，y>0.(2)在(0,+∞)上是增函數(shù)(2)在(0,+∞)上是減函數(shù).5.指數(shù)函數(shù)與對(duì)數(shù)函數(shù)的聯(lián)系與區(qū)別指數(shù)函數(shù)y=ax(a＞0,a≠1)對(duì)數(shù)函數(shù)y=logax(a＞0,a≠1)定義域值域圖象x∈Rx∈(0,+∞)y∈（0，+∞）y∈R.指數(shù)函數(shù)y=ax(a＞0,a≠1)對(duì)數(shù)函數(shù)y=logax(a＞0,a≠1)性質(zhì)過(guò)定點(diǎn)（0，1）過(guò)定點(diǎn)（1，0）減函數(shù)增函數(shù)減函數(shù)增函數(shù)x∈(-∞，0)時(shí)，y∈(1,+∞)x∈(0,+∞)時(shí)，y∈(0,1)x∈(-∞,0)時(shí),y∈(0,1)x∈(0,+∞)時(shí),y∈(1,+∞)x∈(0,1)時(shí)，y∈(0,+∞)x∈(1,+∞)時(shí),y∈(-∞,0)x∈(0,1)時(shí)，y=∈(-∞,0)x∈(1,+∞)時(shí)，