高考數(shù)學(xué)總復(fù)習(xí) 第二章第8課時(shí) 對(duì)數(shù)函數(shù)課件 新人教版

第第8課時(shí)對(duì)數(shù)函數(shù)課時(shí)對(duì)數(shù)函數(shù)第二章基本初等函數(shù)、導(dǎo)數(shù)及其應(yīng)用第二章基本初等函數(shù)、導(dǎo)數(shù)及其應(yīng)用教材回扣教材回扣 夯實(shí)雙基夯實(shí)雙基基礎(chǔ)梳理基礎(chǔ)梳理1.對(duì)數(shù)的概念及運(yùn)算法則對(duì)數(shù)的概念及運(yùn)算法則(1)對(duì)數(shù)的定義對(duì)數(shù)的定義如果如果_那么數(shù)那么數(shù)x叫做叫做以以a為底為底N的對(duì)數(shù)的對(duì)數(shù),記作記作_,其中其中_叫做對(duì)數(shù)的底數(shù)叫做對(duì)數(shù)的底數(shù),_ 叫做真數(shù)叫做真數(shù).axN(a0,且且a1)xlogaNaN思考探究思考探究1.由定義可知對(duì)數(shù)的底數(shù)與真數(shù)的取值由定義可知對(duì)數(shù)的底數(shù)與真數(shù)的取值范圍是什么范圍是什么?提示：提示：底數(shù)大于零且不等于底數(shù)大于零且不等于1,真數(shù)大于真數(shù)大于零零.(2)對(duì)數(shù)的常用關(guān)系式對(duì)數(shù)的常用關(guān)系式 對(duì)數(shù)恒等式：對(duì)數(shù)恒等式：alogaN_; 換底公式：換底公式：_. logab1logba,推廣推廣 logablogbclogcd_. (3)對(duì)數(shù)的運(yùn)算法則對(duì)數(shù)的運(yùn)算法則 如果如果 a0,且且 a1,M0,N0,那么那么 1 loga(MN)_; logaMN_; logaMn_; logamMn_. 思考探究思考探究2.若若MN0,運(yùn)算法則還成立嗎運(yùn)算法則還成立嗎?提示：提示：不一定成立不一定成立.2.對(duì)數(shù)函數(shù)的圖象與性質(zhì)對(duì)數(shù)函數(shù)的圖象與性質(zhì)a10a1時(shí)時(shí),y0當(dāng)當(dāng)0 x1時(shí)時(shí),y0當(dāng)當(dāng)0 x1時(shí)時(shí),_是是(0,)上的上的_是是(0,)上的上的_(0,)R(1,0)y0增函數(shù)增函數(shù)減函數(shù)減函數(shù)3.反函數(shù)反函數(shù)指數(shù)函數(shù)指數(shù)函數(shù)yax(a0且且a1)與對(duì)數(shù)函與對(duì)數(shù)函數(shù)數(shù)ylogax(a0且且a1)互為反函數(shù)互為反函數(shù),它們的圖象關(guān)于直線它們的圖象關(guān)于直線_對(duì)稱對(duì)稱.yx課前熱身課前熱身2.(2010高考浙江卷高考浙江卷)已知函數(shù)已知函數(shù)f(x)log2(x1),若若f()1,則則()A.0 B.1C.2 D.3答案：答案：B3.(2010高考山東卷高考山東卷)函數(shù)函數(shù)f(x)log2(3x1)的值域?yàn)榈闹涤驗(yàn)?)A.(0,) B.0,)C.(1,) D.1,)答案：答案：A答案：答案：205.若函數(shù)若函數(shù)yloga(xb)(a0且且a1)的的圖象過(guò)兩點(diǎn)圖象過(guò)兩點(diǎn)(1,0)和和(0,1),則則ab_.答案：答案：4考點(diǎn)探究考點(diǎn)探究 講練互動(dòng)講練互動(dòng)考點(diǎn)考點(diǎn)1對(duì)數(shù)式的化簡(jiǎn)與求值對(duì)數(shù)式的化簡(jiǎn)與求值(1)化同底是對(duì)數(shù)式變形的首選方向化同底是對(duì)數(shù)式變形的首選方向,其其中經(jīng)常用到換底公式及其推論中經(jīng)常用到換底公式及其推論.(2)結(jié)合對(duì)數(shù)定義結(jié)合對(duì)數(shù)定義,適時(shí)進(jìn)行對(duì)數(shù)式與指適時(shí)進(jìn)行對(duì)數(shù)式與指數(shù)式的互化數(shù)式的互化.(3)利用對(duì)數(shù)運(yùn)算法則利用對(duì)數(shù)運(yùn)算法則,在積、商、冪的在積、商、冪的對(duì)數(shù)與對(duì)數(shù)的和、差、倍之間進(jìn)行轉(zhuǎn)化對(duì)數(shù)與對(duì)數(shù)的和、差、倍之間進(jìn)行轉(zhuǎn)化.例例1【方法指導(dǎo)方法指導(dǎo)】對(duì)數(shù)的運(yùn)算常有兩種解對(duì)數(shù)的運(yùn)算常有兩種解題思路：一是將對(duì)數(shù)的和、差、積、題思路：一是將對(duì)數(shù)的和、差、積、商、冪轉(zhuǎn)化為對(duì)數(shù)真數(shù)的積、商、冪商、冪轉(zhuǎn)化為對(duì)數(shù)真數(shù)的積、商、冪;二是將式子化為最簡(jiǎn)單的對(duì)數(shù)的和、二是將式子化為最簡(jiǎn)單的對(duì)數(shù)的和、差、積、商、冪差、積、商、冪,合并同類項(xiàng)后再進(jìn)行合并同類項(xiàng)后再進(jìn)行運(yùn)算運(yùn)算,解題過(guò)程中解題過(guò)程中,要抓住式子的特點(diǎn)要抓住式子的特點(diǎn),靈靈活使用運(yùn)算法則活使用運(yùn)算法則,如如lg2lg51,lg51lg2等等.互動(dòng)探究互動(dòng)探究考點(diǎn)考點(diǎn)2對(duì)數(shù)函數(shù)的圖象與性質(zhì)對(duì)數(shù)函數(shù)的圖象與性質(zhì)研究對(duì)數(shù)型函數(shù)的圖象時(shí)研究對(duì)數(shù)型函數(shù)的圖象時(shí),一般從最基一般從最基本的對(duì)數(shù)函數(shù)的圖象入手本的對(duì)數(shù)函數(shù)的圖象入手,通過(guò)平移、通過(guò)平移、伸縮、對(duì)稱變換得到對(duì)數(shù)型函數(shù)的圖伸縮、對(duì)稱變換得到對(duì)數(shù)型函數(shù)的圖象象.特別地特別地,要注意底數(shù)要注意底數(shù)a1與與0a0這這一條件一條件,而得到而得到a1的錯(cuò)誤答案的錯(cuò)誤答案,失誤的失誤的原因是沒(méi)有保證原因是沒(méi)有保證u2ax在在0,1上恒上恒為正為正.互動(dòng)探究互動(dòng)探究2.若將本例中的函數(shù)與區(qū)間分別變?yōu)槿魧⒈纠械暮瘮?shù)與區(qū)間分別變?yōu)閒(x)log2(x2axa),(,1,則實(shí)數(shù)則實(shí)數(shù)a的的存在情況如何存在情況如何?方法技巧方法技巧1.指數(shù)式指數(shù)式abN(a0且且a1)與對(duì)數(shù)式與對(duì)數(shù)式logaNb(a0且且a1,N0)的關(guān)系以及的關(guān)系以及這兩種形式的互化是對(duì)數(shù)運(yùn)算法則的關(guān)這兩種形式的互化是對(duì)數(shù)運(yùn)算法則的關(guān)鍵鍵.2.在運(yùn)算性質(zhì)在運(yùn)算性質(zhì)logaMnnlogaM(a0且且a1,M0)時(shí)時(shí),要特別注意條件要特別注意條件,在無(wú)在無(wú)M0的條件下應(yīng)為的條件下應(yīng)為logaMnnloga|M|(nN*,且且n為偶數(shù)為偶數(shù)).4.常見(jiàn)復(fù)合函數(shù)類型常見(jiàn)復(fù)合函數(shù)類型yaf(x)(a0且且a1)ylogaf(x)(a0且且a1)定義定義域域tf(x)的定義域的定義域tf(x)0的解集的解集值域值域先求先求tf(x)的值域的值域,再由再由yat的單調(diào)的單調(diào)性得解性得解先求先求t的取值范圍的取值范圍,再由再由ylogat的單的單調(diào)性得解調(diào)性得解過(guò)定過(guò)定點(diǎn)點(diǎn)令令f(x)0,得得xx0,則過(guò)定點(diǎn)則過(guò)定點(diǎn)(x0,1)令令f(x)1,得得xx0,則過(guò)定點(diǎn)則過(guò)定點(diǎn)(x0,0)單調(diào)單調(diào)區(qū)間區(qū)間先求先求tf(x)的單調(diào)的單調(diào)區(qū)間區(qū)間,再由同增異再由同增異減得解減得解先求使先求使tf(x)0恒恒成立的單調(diào)區(qū)間成立的單調(diào)區(qū)間,再由同增異減得解再由同增異減得解失誤防范失誤防范1.指數(shù)運(yùn)算的實(shí)質(zhì)是指數(shù)式的積、商、指數(shù)運(yùn)算的實(shí)質(zhì)是指數(shù)式的積、商、冪的運(yùn)算冪的運(yùn)算,對(duì)于指數(shù)式的和、差應(yīng)充分對(duì)于指數(shù)式的和、差應(yīng)充分運(yùn)用恒等變形和乘法公式運(yùn)用恒等變形和乘法公式;對(duì)數(shù)運(yùn)算的對(duì)數(shù)運(yùn)算的實(shí)質(zhì)是把積、商、冪的對(duì)數(shù)轉(zhuǎn)化為對(duì)實(shí)質(zhì)是把積、商、冪的對(duì)數(shù)轉(zhuǎn)化為對(duì)數(shù)的和、差、倍數(shù)的和、差、倍.2.指數(shù)函數(shù)指數(shù)函數(shù)yax(a0,且且a1)與對(duì)數(shù)函與對(duì)數(shù)函數(shù)數(shù)ylogax(a0,且且a1)互為反函數(shù)互為反函數(shù),應(yīng)應(yīng)從概念、圖象和性質(zhì)三個(gè)方面理解它們從概念、圖象和性質(zhì)三個(gè)方面理解它們之間的聯(lián)系與區(qū)別之間的聯(lián)系與區(qū)別.3.明確函數(shù)圖象的位置和形狀要通過(guò)研明確函數(shù)圖象的位置和形狀要通過(guò)研究函數(shù)的性質(zhì)究函數(shù)的性質(zhì),要記憶函數(shù)的性質(zhì)可借要記憶函數(shù)的性質(zhì)可借助于函數(shù)的圖象助于函數(shù)的圖象.因此要掌握指數(shù)函數(shù)因此要掌握指數(shù)函數(shù)和對(duì)數(shù)函數(shù)的性質(zhì)首先要熟記指數(shù)函數(shù)和對(duì)數(shù)函數(shù)的性質(zhì)首先要熟記指數(shù)函數(shù)和對(duì)數(shù)函數(shù)的圖象和對(duì)數(shù)函數(shù)的圖象.考向瞭望考向瞭望 把脈高考把脈高考命題預(yù)測(cè)命題預(yù)測(cè)從近幾年的高考試題看從近幾年的高考試題看,對(duì)數(shù)函數(shù)的性對(duì)數(shù)函數(shù)的性質(zhì)是高考的熱點(diǎn)質(zhì)是高考的熱點(diǎn),題型一般為選擇題、題型一般為選擇題、填空題填空題,屬中低檔題屬中低檔題,主要考查利用對(duì)數(shù)主要考查利用對(duì)數(shù)函數(shù)的性質(zhì)比較對(duì)數(shù)值大小函數(shù)的性質(zhì)比較對(duì)數(shù)值大小,求定義域、值域、最值以及對(duì)數(shù)函數(shù)與求定義域、值域、最值以及對(duì)數(shù)函數(shù)與相應(yīng)指數(shù)函數(shù)的關(guān)系相應(yīng)指數(shù)函數(shù)的關(guān)系.預(yù)測(cè)預(yù)測(cè)2013年高考仍將以對(duì)數(shù)函數(shù)的性年高考仍將以對(duì)數(shù)函數(shù)的性質(zhì)為主要考點(diǎn)質(zhì)為主要考點(diǎn),重點(diǎn)考查運(yùn)用知識(shí)解決重點(diǎn)考查運(yùn)用知識(shí)解決問(wèn)題的能力問(wèn)題的能力.典例透析典例透析 例例【答案】【答案】A