1、 研究細(xì)胞分裂時(shí)，曾經(jīng)歸納出，第x次分裂后，細(xì)胞的個(gè)數(shù)為y=2x；給定分裂的次數(shù)x，我們可以求出細(xì)胞個(gè)數(shù)y。有時(shí)我們會(huì)遇到這樣的問題: 已知一個(gè)細(xì)胞分裂x次后細(xì)胞的個(gè)數(shù)是1024，問這個(gè)細(xì)胞分裂了幾次？即：2x=1024，則x=？一、對(duì)數(shù)的定義：一、對(duì)數(shù)的定義：一般地，對(duì)于指數(shù)式一般地，對(duì)于指數(shù)式 ，我們把，我們把“以以a為底為底N的對(duì)的對(duì)數(shù)數(shù)b”記作，記作記作，記作 ，即，即數(shù)數(shù)a叫做叫做對(duì)數(shù)的底數(shù)對(duì)數(shù)的底數(shù)，N叫做叫做真數(shù)真數(shù)，式子，式子 叫做叫做對(duì)數(shù)式。對(duì)數(shù)式。 讀作讀作“b等于以等于以a為底為底N的對(duì)數(shù)的對(duì)數(shù)”。baNlogaNlog(0,1).abN aa且logaNlogabN對(duì)數(shù)

2、等式logaN=b寫為乘方等式就是ab=N,乘方等式ab=N,寫為對(duì)數(shù)等式就是logaN=b但要注意兩式中字母a,N,b的稱呼的異同. logaN=b 就是 ab=N底數(shù)底數(shù)底數(shù)底數(shù)真數(shù)真數(shù)冪冪對(duì)數(shù)對(duì)數(shù)指數(shù)指數(shù)(a0,a1)(a0,a1)二、對(duì)數(shù)與指數(shù)之間的互化二、對(duì)數(shù)與指數(shù)之間的互化三、對(duì)數(shù)三、對(duì)數(shù)logaN（a0且且a1）的性質(zhì)：）的性質(zhì)： （1）0和負(fù)數(shù)沒有對(duì)數(shù)，即和負(fù)數(shù)沒有對(duì)數(shù)，即N0;（2）1的對(duì)數(shù)為的對(duì)數(shù)為0，即，即loga1=0；（3）底的對(duì)數(shù)等于）底的對(duì)數(shù)等于1，即，即logaa=1。以以10為底的對(duì)數(shù)叫做為底的對(duì)數(shù)叫做常用對(duì)數(shù)，為了簡(jiǎn)便，通常把底常用對(duì)數(shù)，為了簡(jiǎn)便，通常把底1

3、0略去不寫，并把略去不寫，并把“l(fā)og”寫成寫成“l(fā)g”，即把，即把如：如：“100的對(duì)數(shù)是的對(duì)數(shù)是2”，就是，就是“100的常用對(duì)數(shù)是的常用對(duì)數(shù)是2”。四、常用對(duì)數(shù)四、常用對(duì)數(shù)五、對(duì)數(shù)恒等式五、對(duì)數(shù)恒等式NaNalog10loglgNN記做典例分析典例分析例1.（1）lg10,lg100,lg0.01求6255464126373 a73. 5)31(m（2）將下列指數(shù)式寫成對(duì)數(shù)式416log217128log2a27log3201. 0lg(3)將下列對(duì)數(shù)式寫成指數(shù)式將下列對(duì)數(shù)式寫成指數(shù)式 2222216422.1(1)log 32 log22 log 43,22,log 3,m naaxxmna例求，2,log 1,log 16,log的值（）的值為_.(3)log則 的值為_.(4)已知log則的值為_.331loglog553.3( 3)例 化簡(jiǎn)四快樂體驗(yàn)四快樂