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)（一）對(duì)數(shù)1對(duì)數(shù)的概念對(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?aNNalog2、兩個(gè)重要對(duì)數(shù)：、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(wú)理數(shù)為底的對(duì)數(shù)的對(duì)數(shù)○2?71828.2?eNln3、對(duì)數(shù)式與指數(shù)式的互化、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)←→

2、冪xN4、對(duì)數(shù)的性質(zhì)、對(duì)數(shù)的性質(zhì)（1）負(fù)數(shù)和零沒(méi)有對(duì)數(shù)；（2）1的對(duì)數(shù)是零：；01log?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?log5、對(duì)數(shù)的運(yùn)算法則、對(duì)數(shù)的運(yùn)算法則：????logloglogaaaMNMNMNR????，??logloglogaaaMNMNMNR????，????logloganaNnNNR?????logloganaNnNNR???16、對(duì)數(shù)換底公式：、對(duì)數(shù)換

3、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)27182810由換底公式推出一些常用的結(jié)論：3對(duì)數(shù)函數(shù)的性質(zhì)：○2圖象特征函數(shù)性質(zhì)1a?1a0??1a?1a0??函數(shù)圖象都在y軸右側(cè)函數(shù)的定義域?yàn)椋?，＋∞）圖象關(guān)于原點(diǎn)和y軸不對(duì)稱非奇非偶函數(shù)向y軸正負(fù)方向無(wú)限延伸函數(shù)的值域?yàn)镽函數(shù)圖象都過(guò)定點(diǎn)（1，1）11??自左向右看，圖象逐漸上升自左向右看，圖象逐漸下降增函數(shù)