對(duì)數(shù)函數(shù)知識(shí)點(diǎn)總結(jié)

1、對(duì)數(shù)函數(shù)對(duì)數(shù)函數(shù)（一）對(duì)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)，Nax?)10(??aaxaN記作：（—底數(shù)，—真數(shù)，—對(duì)數(shù)式）Nxalog?aNNalog說(shuō)明：注意底數(shù)的限制，且；○10?a1?a；○2xNNaax???log注意對(duì)數(shù)的書寫格式○3兩個(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)○2?71828.2?e數(shù)Nln（二）對(duì)數(shù)的運(yùn)算性質(zhì)如果，且，，，那么：0?a1?a0?M0

2、?N＋；○1Ma(log?)NMalogNalog－；○2?NMalogMalogNalog○3naMlogn?Malog)(Rn?注意：換底公式（，且；，且；abbccalogloglog?0?a1?a0?c1?c）0?b利用換底公式推導(dǎo)下面的結(jié)論（1）；（2）bmnbanamloglog?abbalog1log?（二）對(duì)數(shù)函數(shù)1、對(duì)數(shù)函數(shù)的概念：函數(shù)，且叫做對(duì)數(shù)0(log??axya)1?a函數(shù)，其中是自變量，函數(shù)的定義域是（0，∞

3、）x注意：對(duì)數(shù)函數(shù)的定義與指數(shù)函數(shù)類似，都是形式定義，注○1意辨別。如：，都不是對(duì)數(shù)函數(shù)，而只能xy2log2?5log5xy?稱其為對(duì)數(shù)型函數(shù)對(duì)數(shù)函數(shù)對(duì)底數(shù)的限制：，且○20(?a)1?a2、對(duì)數(shù)函數(shù)的性質(zhì)：a10a132.521.510.50.511.522.511234567801132.521.510.50.511.522.5112345678011定義域x＞0定義域x＞0值域?yàn)镽值域?yàn)镽在R上遞增在R上遞減函數(shù)圖象都函數(shù)圖象都

4、過(guò)定點(diǎn)例5比較下列比較下列各組數(shù)中兩個(gè)值的大?。海?），；（2），；6log77log63log?2log0.8（3），，；（4），，0.91.11.1log0.90.7log0.85log36log37log3解：（1）∵，，∴；66log7log61??77log6log71??6log7?7log6（2）∵，，∴33loglog10???22log0.8log10??3log??2log0.8(3）∵，，0.901.11.11??

5、1.11.1log0.9log10??，0.70.70.70log1log0.8log0.71????∴0.91.1?0.7log0.8?1.1log0.9（4）∵，∴3330log5log6log7???5log3?6log3?7log3例7求下列函數(shù)的值域：（1）；（2）；（3）2log(3)yx??22log(3)yx??（且）2log(47)ayxx???0a?1a?解：（1）令，則，∵，∴，即函數(shù)值域?yàn)?tx??2logyt?