高一數(shù)學(xué)對(duì)數(shù)及對(duì)數(shù)函數(shù)知識(shí)點(diǎn)及習(xí)題

1、1對(duì)數(shù)及對(duì)數(shù)函數(shù)1對(duì)數(shù)的概念一般地，如果，那么數(shù)叫做以為底的對(duì)數(shù)，記作：Nax?)10(??aaxaN其中：是底數(shù)，是真數(shù)，是對(duì)數(shù)式Nxalog?aNNalog兩個(gè)重要對(duì)數(shù)：常用對(duì)數(shù)：以10為底的對(duì)數(shù)；○1Nlg自然對(duì)數(shù)：以無理數(shù)為底的對(duì)數(shù)的對(duì)數(shù)○2?71828.2?eNln對(duì)數(shù)式與指數(shù)式的互化xNa?log?Nax?對(duì)數(shù)式指數(shù)式對(duì)數(shù)底數(shù)←→冪底數(shù)?a對(duì)數(shù)←→指數(shù)真數(shù)←→冪xN對(duì)數(shù)的性質(zhì)（1）負(fù)數(shù)和零沒有對(duì)數(shù)；（2）1的對(duì)數(shù)是零：；01

2、log?a（3）底數(shù)的對(duì)數(shù)是1：；（4）對(duì)數(shù)恒等式：；1log?aaNaNa?log（5）nana?log對(duì)數(shù)的運(yùn)算法則：????logloglogaaaMNMNMNR????，??logloglogaaaMNMNMNR????，????logloganaNnNNR?????logloganaNnNNR???1對(duì)數(shù)換底公式：loglogloglog(.)logbaanegNNbLNNeNLNN????其中…稱為的自然對(duì)數(shù)稱為常數(shù)對(duì)數(shù)27

3、182810由換底公式推出一些常用的結(jié)論：（1）（2）loglogloglogababbaba??11或loglogamanbmnb?（3）（4）loglogananbb?logamnamn?3Ababa???12Bbaba???12Cbaba???12Dbaba???124.函數(shù)y=)12(log21?x的定義域?yàn)椋ǎ〢(21，＋∞)B［1，＋∞)C(21，1]D(－∞，1)5.已知f(ex)=x，則f(5)等于（）Ae5B5eCln