4.4.1

對(duì)數(shù)函數(shù)的概念

4.4.2

對(duì)數(shù)函數(shù)的圖象和性質(zhì)課標(biāo)闡釋思維脈絡(luò)1.通過(guò)具體實(shí)例,了解對(duì)數(shù)函數(shù)的概念.(數(shù)學(xué)抽象)2.能用描點(diǎn)法或借助計(jì)算工具畫(huà)出具體對(duì)數(shù)函數(shù)的圖象,探索并了解對(duì)數(shù)函數(shù)的單調(diào)性與特殊點(diǎn).(直觀(guān)想象)3.知道對(duì)數(shù)函數(shù)y=logax與指數(shù)函數(shù)y=ax互為反函數(shù)(a>0,且a≠1).(數(shù)學(xué)抽象)激趣誘思知識(shí)點(diǎn)撥某種物質(zhì)的細(xì)胞分裂,由1個(gè)分裂成2個(gè),2個(gè)分裂成4個(gè),……,則1個(gè)這樣的細(xì)胞分裂x次后得到的細(xì)胞個(gè)數(shù)y如何表示?(y=2x)那么如果知道這種物質(zhì)的一個(gè)細(xì)胞經(jīng)過(guò)x次分裂后得到了1024個(gè)細(xì)胞,如何求解x的值呢?激趣誘思知識(shí)點(diǎn)撥知識(shí)點(diǎn)一、對(duì)數(shù)函數(shù)1.對(duì)數(shù)函數(shù)的概念(2)指數(shù)函數(shù)y=ax(a>0,且a≠1)與對(duì)數(shù)函數(shù)y=logax(a>0,且a≠1)互為反函數(shù).兩者的定義域與值域正好互換.2.兩種特殊的對(duì)數(shù)特別地,我們稱(chēng)以10為底的對(duì)數(shù)函數(shù)為常用對(duì)數(shù)函數(shù),記作y=lgx;稱(chēng)以無(wú)理數(shù)e為底的對(duì)數(shù)函數(shù)為自然對(duì)數(shù)函數(shù),記作y=lnx.激趣誘思知識(shí)點(diǎn)撥名師點(diǎn)析

1.判斷一個(gè)函數(shù)是不是對(duì)數(shù)函數(shù)的依據(jù):(1)形如y=logax;(2)底數(shù)a滿(mǎn)足a>0,且a≠1;(3)真數(shù)為x,而不是x的函數(shù).2.根據(jù)指數(shù)式與對(duì)數(shù)式的關(guān)系知,y=logax可化為ay=x,由指數(shù)函數(shù)的性質(zhì)可知在對(duì)數(shù)函數(shù)中,有a>0且a≠1,x>0,y∈R.3.同底的指數(shù)函數(shù)與對(duì)數(shù)函數(shù)互為反函數(shù),它們的圖象關(guān)于直線(xiàn)y=x對(duì)稱(chēng).反函數(shù)的定義域是原函數(shù)的值域,反函數(shù)的值域是原函數(shù)的定義域.4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)激趣誘思知識(shí)點(diǎn)撥微練習(xí)1下列函數(shù)是對(duì)數(shù)函數(shù)的是(

)A.y=logax+2(a>0,且a≠1,x>0)B.y=log2(x>0)C.y=logx3(x>0,且x≠1)D.y=log6x(x>0)答案:D4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)激趣誘思知識(shí)點(diǎn)撥微拓展1.若函數(shù)y=f(x)圖象上有一點(diǎn)(a,b),則點(diǎn)(b,a)必在其反函數(shù)圖象上;反之亦然.2.單調(diào)函數(shù)的反函數(shù)與原函數(shù)有相同的單調(diào)性.3.若一個(gè)奇函數(shù)存在反函數(shù),則這個(gè)反函數(shù)也是奇函數(shù).微練習(xí)24.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)激趣誘思知識(shí)點(diǎn)撥知識(shí)點(diǎn)二、對(duì)數(shù)函數(shù)y=logax(a>0,且a≠1)的圖象和性質(zhì)

a>10<a<1圖象4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)激趣誘思知識(shí)點(diǎn)撥

a>10<a<1性質(zhì)(1)定義域:(0,+∞)(2)值域:R(3)過(guò)定點(diǎn)(1,0),即x=1時(shí),y=0(4)當(dāng)x>1時(shí),y>0;0<x<1時(shí),y<0(4)當(dāng)x>1時(shí),y<0;0<x<1時(shí),y>0(5)在(0,+∞)上是增函數(shù).當(dāng)x值趨近于正無(wú)窮大時(shí),函數(shù)值趨近于正無(wú)窮大;當(dāng)x值趨近于0時(shí),函數(shù)值趨近于負(fù)無(wú)窮大(5)在(0,+∞)上是減函數(shù).當(dāng)x值趨近于正無(wú)窮大時(shí),函數(shù)值趨近于負(fù)無(wú)窮大;當(dāng)x值趨近于0時(shí),函數(shù)值趨近于正無(wú)窮大4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)激趣誘思知識(shí)點(diǎn)撥名師點(diǎn)析

(1)對(duì)數(shù)函數(shù)的圖象永遠(yuǎn)在y軸的右側(cè),y軸可以看成對(duì)數(shù)函數(shù)的漸近線(xiàn),x越接近于0,圖象越接近y軸.(2)對(duì)數(shù)函數(shù)的符號(hào)常受到底數(shù)和真數(shù)的范圍的制約,注意對(duì)底數(shù)a的分類(lèi)討論.(3)當(dāng)?shù)讛?shù)a>1時(shí),圖象在第一象限內(nèi)越接近x軸,a越大;當(dāng)?shù)讛?shù)0<a<1時(shí),圖象在第四象限內(nèi)越接近x軸,a越小.(4)分析對(duì)數(shù)函數(shù)y=logax(a>0,且a≠1)的圖象,需找三個(gè)關(guān)鍵點(diǎn):(a,1),(1,0),4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)激趣誘思知識(shí)點(diǎn)撥微練習(xí)1(多選題)若函數(shù)y=logax的圖象如圖所示,則a的值可能是(

)A.0.3

D.π答案:AB4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)激趣誘思知識(shí)點(diǎn)撥微練習(xí)2(1)下列函數(shù)中,在區(qū)間(0,+∞)內(nèi)不是增函數(shù)的是(

)A.y=5x

B.y=lgx+2C.y=x2+1 (2)函數(shù)f(x)=loga(x-2)-2x的圖象必經(jīng)過(guò)定點(diǎn)

.

答案:(1)D

(2)(3,-6)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)對(duì)數(shù)函數(shù)的概念例1(1)已知對(duì)數(shù)函數(shù)f(x)=(m2-3m+3)·logmx,則m=

.

①求f(x)的解析式;②解方程f(x)=2.分析(1)根據(jù)對(duì)數(shù)函數(shù)的形式定義確定參數(shù)m所滿(mǎn)足的條件求解即可;(2)根據(jù)已知設(shè)出函數(shù)解析式,代入點(diǎn)的坐標(biāo)求出對(duì)數(shù)函數(shù)的底數(shù),然后利用指對(duì)互化解方程.4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)(1)解析:由對(duì)數(shù)函數(shù)的定義可得m2-3m+3=1,即m2-3m+2=0,也就是(m-1)(m-2)=0,解得m=1或m=2.又因?yàn)閙>0,且m≠1,所以m=2.答案:24.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)反思感悟

1.對(duì)數(shù)函數(shù)是一個(gè)形式定義:2.對(duì)數(shù)函數(shù)解析式中只有一個(gè)參數(shù)a,用待定系數(shù)法求對(duì)數(shù)函數(shù)解析式時(shí)只需一個(gè)條件即可求出.4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)變式訓(xùn)練1(1)若函數(shù)f(x)=log(a+1)x+(a2-2a-8)是對(duì)數(shù)函數(shù),則a=

.

(2)點(diǎn)A(8,-3)和B(n,2)在同一個(gè)對(duì)數(shù)函數(shù)圖象上,則n=

.

探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)與對(duì)數(shù)函數(shù)有關(guān)的定義域、值域問(wèn)題例2(1)函數(shù)f(x)=ln(x2-x)的定義域?yàn)?

)A.(-∞,0)∪(1,+∞)B.(-∞,0]∪[1,+∞)C.(0,1)D.[0,1]探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)解析:(1)由題意得x2-x>0,解得x>1或x<0,故函數(shù)f(x)的定義域是(-∞,0)∪(1,+∞).故選A.探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)反思感悟

定義域問(wèn)題注意事項(xiàng)(1)要遵循以前已學(xué)習(xí)過(guò)的求定義域的方法,如分式分母不為零,偶次根式被開(kāi)方式大于或等于零等.(2)遵循對(duì)數(shù)函數(shù)自身的要求:一是真數(shù)大于零;二是底數(shù)大于零且不等于1;三是按底數(shù)的取值應(yīng)用單調(diào)性,有針對(duì)性地解不等式.探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)指數(shù)函數(shù)與對(duì)數(shù)函數(shù)關(guān)系的應(yīng)用例3(2020四川宜賓高一檢測(cè))已知函數(shù)f(x)=log2x,若函數(shù)g(x)是f(x)的反函數(shù),則f(g(2))=(

)A.1 B.2 C.3 D.4解析:∵g(x)是f(x)的反函數(shù),∴g(x)=2x.∵g(2)=22=4,∴f(g(2))=f(4)=log24=2.答案:B反思感悟

涉及指數(shù)和對(duì)數(shù)函數(shù)互為反函數(shù)問(wèn)題,一定注意前提是“同底數(shù)”,且它們的圖象關(guān)于直線(xiàn)y=x對(duì)稱(chēng);反之,兩個(gè)函數(shù)圖象關(guān)于直線(xiàn)y=x對(duì)稱(chēng),則這兩個(gè)函數(shù)互為反函數(shù).探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)變式訓(xùn)練2已知函數(shù)g(x)=f(x)+x2是奇函數(shù),當(dāng)x>0時(shí),函數(shù)f(x)的圖象與函數(shù)y=log2x的圖象關(guān)于直線(xiàn)y=x對(duì)稱(chēng),則g(-1)+g(-2)=(

)A.-7 B.-9 C.-11 D.-13解析:由題意知當(dāng)x>0時(shí),f(x)=2x,則當(dāng)x>0時(shí),g(x)=2x+x2.∵g(x)為奇函數(shù),∴g(-1)=-g(1)=-3,g(-2)=-g(2)=-8.∴g(-1)+g(-2)=-11.答案:C探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)對(duì)數(shù)函數(shù)的圖象例4函數(shù)y=log2x,y=log5x,y=lgx的圖象如圖所示.(1)說(shuō)明哪個(gè)函數(shù)對(duì)應(yīng)于哪個(gè)圖象,并說(shuō)明理由;(3)從(2)的圖中你發(fā)現(xiàn)了什么?探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)解:(1)①對(duì)應(yīng)函數(shù)y=lg

x,②對(duì)應(yīng)函數(shù)y=log5x,③對(duì)應(yīng)函數(shù)y=log2x.這是因?yàn)楫?dāng)?shù)讛?shù)全大于1時(shí),在x=1的右側(cè),底數(shù)越大的函數(shù)圖象越靠近x軸.(2)在題圖中的平面直角坐標(biāo)系中分別畫(huà)出4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)反思感悟

對(duì)數(shù)函數(shù)圖象的變化規(guī)律:1.對(duì)于幾個(gè)底數(shù)都大于1的對(duì)數(shù)函數(shù),底數(shù)越大,函數(shù)圖象向右的方向越接近x軸;對(duì)于幾個(gè)底數(shù)都大于0且小于1的對(duì)數(shù)函數(shù),底數(shù)越大,函數(shù)圖象向右的方向越遠(yuǎn)離x軸.以上規(guī)律可總結(jié)成x>1時(shí)“底大圖低”.實(shí)際上,作出直線(xiàn)y=1,它與各圖象交點(diǎn)的橫坐標(biāo)即為各函數(shù)的底數(shù)的大小,如圖所示.2.牢記特殊點(diǎn):對(duì)數(shù)函數(shù)y=logax(a>0,且a≠1)的圖象經(jīng)過(guò)(1,0),(a,1),4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)變式訓(xùn)練3作出函數(shù)y=|lg(x-1)|的圖象,并根據(jù)圖象寫(xiě)出函數(shù)的定義域、值域以及單調(diào)區(qū)間.解:先畫(huà)出函數(shù)y=lg

x的圖象(如圖①).再將該函數(shù)圖象向右平移1個(gè)單位長(zhǎng)度得到函數(shù)y=lg(x-1)的圖象(如圖②).圖①圖②4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)最后把y=lg(x-1)的圖象在x軸下方的部分對(duì)稱(chēng)翻折到x軸上方(原來(lái)在x軸上方的部分不變),即得出函數(shù)y=|lg(x-1)|的圖象(如圖③).由圖易知其定義域?yàn)?1,+∞),值域?yàn)閇0,+∞),單調(diào)遞減區(qū)間為(1,2],單調(diào)遞增區(qū)間為(2,+∞).4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)數(shù)函數(shù)的性質(zhì)比較大小例5比較下列各組中兩個(gè)值的大小:(1)log31.9,log32;(2)log23,log0.32;(3)logaπ,loga3.141(a>0,且a≠1).分析(1)構(gòu)造函數(shù)f(x)=log3x,利用其單調(diào)性比較大小;(2)分別比較兩個(gè)對(duì)數(shù)與0的大小;(3)分類(lèi)討論底數(shù)a的取值范圍,再利用單調(diào)性比較大小.4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)解:(1)(單調(diào)性法)因?yàn)閒(x)=log3x在(0,+∞)上是增函數(shù),且1.9<2,所以f(1.9)<f(2),即log31.9<log32.(2)(中間量法)因?yàn)閘og23>log21=0,log0.32<log0.31=0,所以log23>log0.32.(3)(分類(lèi)討論法)當(dāng)a>1時(shí),函數(shù)y=logax在定義域內(nèi)是增函數(shù),則有l(wèi)ogaπ>loga3.141;當(dāng)0<a<1時(shí),函數(shù)y=logax在定義域內(nèi)是減函數(shù),則有l(wèi)ogaπ<loga3.141.綜上所述,當(dāng)a>1時(shí),logaπ>loga3.141;當(dāng)0<a<1時(shí),logaπ<loga3.141.4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)反思感悟

比較兩個(gè)對(duì)數(shù)式大小的常用方法(1)當(dāng)?shù)讛?shù)相同,真數(shù)不相同時(shí),直接利用對(duì)數(shù)函數(shù)的單調(diào)性進(jìn)行比較.(2)當(dāng)?shù)讛?shù)不同,真數(shù)相同時(shí),可根據(jù)圖象與底數(shù)的關(guān)系所反映出的規(guī)律比較,常數(shù)形結(jié)合.(3)當(dāng)?shù)讛?shù)和真數(shù)都不相同時(shí),可考慮引進(jìn)第三個(gè)數(shù)(常用“0”或“1”)分別與之比較,通過(guò)第三個(gè)數(shù)的傳遞比較.4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)變式訓(xùn)練4比較下列各組中兩個(gè)值的大小:(1)ln0.3,ln2;(2)loga3.1,loga5.2(a>0,且a≠1);(3)log30.2,log40.2;(4)log3π,logπ3.解:(1)因?yàn)楹瘮?shù)y=ln

x在定義域內(nèi)是增函數(shù),且0.3<2,所以ln

0.3<ln

2.(2)當(dāng)a>1時(shí),函數(shù)y=logax在(0,+∞)上是增函數(shù),又3.1<5.2,所以loga3.1<loga5.2;當(dāng)0<a<1時(shí),函數(shù)y=logax在(0,+∞)上是減函數(shù),又3.1<5.2,所以loga3.1>loga5.2.故當(dāng)a>1時(shí),loga3.1<loga5.2;當(dāng)0<a<1時(shí),loga3.1>loga5.2.4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)(方法二)畫(huà)出y=log3x與y=log4x的圖象,如圖所示,由圖可知log40.2>log30.2.(4)因?yàn)楹瘮?shù)y=log3x在定義域內(nèi)是增函數(shù),且π>3,所以log3π>log33=1.同理,1=logππ>logπ3,所以log3π>logπ3.4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)與對(duì)數(shù)函數(shù)有關(guān)的創(chuàng)新問(wèn)題性質(zhì),取得部分研究結(jié)果如下:①函數(shù)f(x)的定義域?yàn)?-1,1);②函數(shù)f(x)是偶函數(shù);4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)4.4.1對(duì)數(shù)函數(shù)的概念4.4.2對(duì)數(shù)函數(shù)的圖象和性質(zhì)-人教A版（2019）高中數(shù)學(xué)必修（第一冊(cè)）課件(共43張PPT)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)探究一探究二探究三探究四探究五素養(yǎng)形成當(dāng)堂檢測(cè)答案: