對(duì)數(shù)函數(shù)的圖像與性質(zhì)公開(kāi)課99472769課件

對(duì)數(shù)函數(shù)的圖像與性質(zhì)目錄?

對(duì)數(shù)函數(shù)與其他函數(shù)的關(guān)系?

課堂練習(xí)與思考對(duì)數(shù)函數(shù)的概念對(duì)數(shù)函數(shù)的定義對(duì)數(shù)函數(shù)的表示方法對(duì)數(shù)函數(shù)通常用log表示，其后面跟著底數(shù)a和真數(shù)x，即logax。當(dāng)a為10時(shí)，常用lgx表示對(duì)數(shù)函數(shù)；當(dāng)a為e時(shí)，常用lnx表示對(duì)數(shù)函數(shù)。VS對(duì)數(shù)函數(shù)的定義域與值域?qū)?shù)函數(shù)的圖像對(duì)數(shù)函數(shù)圖像的基本形狀對(duì)數(shù)函數(shù)圖像的變化趨勢(shì)當(dāng)?shù)讛?shù)a大于1時(shí)，函數(shù)圖像在x軸上方；當(dāng)?shù)讛?shù)a小于1時(shí)，函數(shù)圖像在x軸下方。對(duì)數(shù)函數(shù)圖像的對(duì)稱性對(duì)數(shù)函數(shù)圖像關(guān)于y軸對(duì)稱。對(duì)于任意的實(shí)數(shù)x，都有l(wèi)og_a(x)=log_a(-x)。對(duì)數(shù)函數(shù)的性質(zhì)對(duì)數(shù)函數(shù)的單調(diào)性嚴(yán)格單調(diào)對(duì)于函數(shù)$y=\log_{a}x$，當(dāng)$a>1$時(shí)，函數(shù)在$(0,+\infty)$上嚴(yán)格單調(diào)遞增；當(dāng)$0<a<1$時(shí)，函數(shù)在$(0,+\infty)$上嚴(yán)格單調(diào)遞減?；酱螅鲩L(zhǎng)越快對(duì)于函數(shù)$y=\log_{a}x$，當(dāng)$x$增大時(shí)，如果$a$越大，那么函數(shù)值增長(zhǎng)越快。對(duì)數(shù)函數(shù)的奇偶性奇函數(shù)圖像關(guān)于原點(diǎn)對(duì)稱對(duì)于奇函數(shù)$y=\log_{a}x$，其圖像關(guān)于原點(diǎn)對(duì)稱。對(duì)數(shù)函數(shù)的不等式性質(zhì)$\log_{a}1

=

0$$\log_{a}a

=

1$$\log_{a}{m^n}=n\log_{a}m$對(duì)數(shù)函數(shù)的應(yīng)用對(duì)數(shù)函數(shù)在復(fù)利計(jì)算中的應(yīng)用復(fù)利計(jì)算的概念010203對(duì)數(shù)函數(shù)在復(fù)利計(jì)算中的重要性復(fù)利公式的推導(dǎo)對(duì)數(shù)函數(shù)在物理學(xué)中的應(yīng)用熱力學(xué)中的對(duì)數(shù)函數(shù)電磁學(xué)中的對(duì)數(shù)函數(shù)彈性力學(xué)中的對(duì)數(shù)函數(shù)對(duì)數(shù)函數(shù)在統(tǒng)計(jì)學(xué)中的應(yīng)用概率論中的對(duì)數(shù)函數(shù)統(tǒng)計(jì)分析中的對(duì)數(shù)函數(shù)對(duì)數(shù)函數(shù)與其他函數(shù)的關(guān)系對(duì)數(shù)函數(shù)與指數(shù)函數(shù)的關(guān)系對(duì)數(shù)函數(shù)和指數(shù)函數(shù)互為反函數(shù)，它們的圖像關(guān)于直線y=x對(duì)稱。對(duì)數(shù)函數(shù)和指數(shù)函數(shù)的定義域和值域也互為反函數(shù)，即如果一個(gè)函數(shù)的定義域是另一個(gè)函數(shù)的值域，那么它們互為反函數(shù)。對(duì)數(shù)函數(shù)和指數(shù)函數(shù)的單調(diào)性也相反，即如果一個(gè)函數(shù)在某個(gè)區(qū)間內(nèi)單調(diào)遞增（或遞減），那么另一個(gè)函數(shù)在該區(qū)間內(nèi)單調(diào)遞減（或遞增）。對(duì)數(shù)函數(shù)與冪函數(shù)的關(guān)系對(duì)數(shù)函數(shù)和冪函數(shù)都是基于冪運(yùn)算的函數(shù)，但是它們的定義域和值域不同。對(duì)數(shù)函數(shù)是以自然對(duì)數(shù)的底數(shù)為底數(shù)，冪函數(shù)則是以任意正實(shí)數(shù)為底數(shù)。對(duì)數(shù)函數(shù)和冪函數(shù)的單調(diào)性也不同，對(duì)數(shù)函數(shù)在定義域內(nèi)單調(diào)遞增（或遞減），而冪函數(shù)則在其定義域內(nèi)既可單調(diào)遞增也可單調(diào)遞減。對(duì)數(shù)函數(shù)與對(duì)勾函數(shù)的關(guān)系010203課堂練習(xí)與思考練習(xí)題一：對(duì)數(shù)函數(shù)的定義域求解總結(jié)詞詳細(xì)描述練習(xí)題二：對(duì)數(shù)函數(shù)的單調(diào)區(qū)間求解總結(jié)詞詳細(xì)描述練習(xí)題三：對(duì)數(shù)函數(shù)的應(yīng)用題求解總結(jié)詞詳細(xì)描述掌握對(duì)數(shù)函數(shù)的應(yīng)用題解題思路對(duì)數(shù)函數(shù)在實(shí)際生活中