高三復(fù)習(xí)學(xué)案對(duì)數(shù)與對(duì)數(shù)函數(shù)

1、1對(duì)數(shù)與對(duì)數(shù)函數(shù)對(duì)數(shù)與對(duì)數(shù)函數(shù)一基礎(chǔ)知識(shí)一基礎(chǔ)知識(shí)1對(duì)數(shù)對(duì)數(shù)(1)對(duì)數(shù)的概念如果那么b叫做以a為底N的對(duì)數(shù)記)10(???aaNab)10(log???aaNba(2)對(duì)數(shù)的性質(zhì)：①零與負(fù)數(shù)沒(méi)有對(duì)數(shù)②③01log?a1log?aa(3)對(duì)數(shù)的運(yùn)算性質(zhì)NMMN①aaalogloglog??NMNM①aaalogloglog??其中a0a≠0M0N0MnM①analoglog?(4)對(duì)數(shù)換底公式：)10100(logloglog??????

2、mmaaNaNNmma且且2對(duì)數(shù)函數(shù)對(duì)數(shù)函數(shù)一般形式：y=x(a0且a≠1)alog定義域：(0∞)值域：(0∞)過(guò)定點(diǎn)：（1，0）圖象：?jiǎn)握{(diào)性：a1在(∞∞)上為增函數(shù)０＜a0當(dāng)y0時(shí)且101???xa時(shí)且1010????xa3.記住常見(jiàn)對(duì)數(shù)函數(shù)的圖形及相互關(guān)系記住常見(jiàn)對(duì)數(shù)函數(shù)的圖形及相互關(guān)系二、題型剖析二、題型剖析1對(duì)數(shù)式的化簡(jiǎn)和運(yùn)算對(duì)數(shù)式的化簡(jiǎn)和運(yùn)算題組題組①指數(shù)式與對(duì)數(shù)式的互化指數(shù)式與對(duì)數(shù)式的互化⑴將下列指數(shù)式改寫成對(duì)數(shù)式；；；

3、；1624?27133??205?a45.021???????b3⑵若，則的取值范圍是【】143log?aaABCD)430()43(??)143()430()1(???5對(duì)數(shù)函數(shù)的性質(zhì)對(duì)數(shù)函數(shù)的性質(zhì)例4.4.已知函數(shù)已知函數(shù)是實(shí)數(shù)集是實(shí)數(shù)集上的奇函數(shù)，且當(dāng)上的奇函數(shù)，且當(dāng)時(shí)，時(shí)，??xfR0?x????1log2??xxf（其中（其中且）0?a1?a⑴求函數(shù)求函數(shù)的解析式；的解析式；⑵畫出函數(shù)畫出函數(shù)的圖像；的圖像；⑶當(dāng)時(shí)，寫出時(shí)，寫

4、出的范圍的范圍??xf??xf??1?xfx例5.5.已知函數(shù)已知函數(shù)＝.??xf??100log?????ababxbxa且⑴求的定義域；的定義域；⑵判斷判斷的奇偶性；的奇偶性；⑶討論討論的單調(diào)性。的單調(diào)性。??xf??xf??xf6.綜合運(yùn)用綜合運(yùn)用⑴已知已知，，試比較，試比較與的大小的大小??3log1xxf????2log2xxg???xf??xg⑵已知是奇函數(shù)（其中，11log)(???xmxxfa)10??aa（1）求的值；