對數(shù)與對數(shù)函數(shù)課件

2.7對數(shù)與對數(shù)函數(shù)2.7對數(shù)與對數(shù)函數(shù)1.對數(shù)的概念(1)對數(shù)的定義如果ax=N(a>0且a≠1)，那么數(shù)x叫做以a為底N的對數(shù),記作_________,其中____叫做對數(shù)的底數(shù),____叫做真數(shù).Nx=logaNa對數(shù)形式特點(diǎn)記法一般對數(shù)底數(shù)為a(a>0且a≠1)_______常用對數(shù)底數(shù)為__________自然對數(shù)底數(shù)為__________lnNlgNlogaN(2)幾種常見對數(shù)10e憶一憶知識要點(diǎn)1.對數(shù)的概念(1)對數(shù)的定義Nx=logaNa對數(shù)形式特2.對數(shù)的性質(zhì)與運(yùn)算法則(1)對數(shù)的性質(zhì)①負(fù)數(shù)和零沒有對數(shù);②logaa

=1；③loga1=0.憶一憶知識要點(diǎn)(2)積、商、冪的對數(shù)運(yùn)算法則：(a>0,且a

1,M>0,N>0)2.對數(shù)的性質(zhì)與運(yùn)算法則(1)對數(shù)的性質(zhì)①負(fù)數(shù)和零沒有對數(shù)2.對數(shù)的性質(zhì)與運(yùn)算法則(3)對數(shù)的重要公式1)對數(shù)的換底公式3)四個(gè)重要推論憶一憶知識要點(diǎn)2)對數(shù)恒等式2.對數(shù)的性質(zhì)與運(yùn)算法則(3)對數(shù)的重要公式1)對數(shù)的換函數(shù)y=logax(a＞0且a≠1)圖象定義域值域單調(diào)性過定點(diǎn)趨勢取值范圍(0,+∞)R增函數(shù)(1，0)底數(shù)越大，圖象越靠近x軸0<x<1時(shí),y<0x>1時(shí),y>00<x<1時(shí),y>0x>1時(shí),y<0底數(shù)越小，圖象越靠近x軸(1，0)減函數(shù)R(0,+∞)3.對數(shù)函數(shù)圖象與性質(zhì)函數(shù)y=logax(a＞0且a≠1指數(shù)函數(shù)y=ax與對數(shù)函數(shù)_________互為反函數(shù),它們的圖象關(guān)于直線_________對稱.y=logaxy=x4.反函數(shù)5.第一象限中,對數(shù)函數(shù)底數(shù)與圖象的關(guān)系圖象從左到右,底數(shù)逐漸變大.憶一憶知識要點(diǎn)指數(shù)函數(shù)y=ax與對數(shù)函數(shù)_________互為反函練習(xí)題練習(xí)題對數(shù)與對數(shù)函數(shù)課件對數(shù)與對數(shù)函數(shù)課件6.已知函數(shù)f(x)＝|lgx|.若a≠b，且f(a)＝f(b)，則a＋b的取值范圍是()A．(1，＋∞) B．[1，＋∞)C．(2，＋∞) D．[2，＋∞)6.已知函數(shù)f(x)＝|lgx|.若a≠b，且f(a)＝f(對數(shù)與對數(shù)函數(shù)課件對數(shù)與對數(shù)函數(shù)課件(4)命題等價(jià)于x2－2ax＋3>0的解集為{x|x<1或x>3}∴x2－2ax＋3＝0的兩根為1和3，∴2a＝1＋3即a＝2(4)命題等價(jià)于x2－2ax＋3>0的解集為{x|x<1或x對數(shù)與對數(shù)函數(shù)課件9.已知函數(shù)f(x)＝loga(x＋1)(a>1),若函數(shù)y＝g(x)圖象上任意一點(diǎn)P關(guān)于原點(diǎn)對稱的點(diǎn)Q的軌跡恰好是函數(shù)f(x)的圖象.(1)寫出函數(shù)g(x)的解析式；(2)當(dāng)x∈[0,1)時(shí)總有f(x)＋g(x)≥m成立,求m的取值范圍.9.已知函數(shù)f(x)＝loga(x＋1)(a>1),若函數(shù)本題的求解體現(xiàn)了方程思想和函數(shù)思想的應(yīng)用,主要涉及對數(shù)式的求值，對數(shù)函數(shù)的圖象和性質(zhì)的綜合運(yùn)用以及與其他知識的結(jié)合(如不等式、指數(shù)函數(shù)等)．本題的求解體現(xiàn)了方程思想和函數(shù)思想的應(yīng)用,主9.已知函數(shù)f(x)＝loga(x＋1)(a>1),若函數(shù)y＝g(x)圖象上任意一點(diǎn)P關(guān)于原點(diǎn)對稱的點(diǎn)Q的軌跡恰好是函數(shù)f(x)的圖象.(1)寫出函數(shù)g(x)的解析式；(2)當(dāng)x∈[0,1)時(shí)總有f(x)＋g(x)≥m成立,求m的取值范圍.9.已知函數(shù)f(x)＝loga(x＋1)(a>1)對數(shù)與對數(shù)函數(shù)課件CA.（1，10）B.（5，6）C.（10，12）D.（20，24）CA.（1，10）B.（5，6）C.（10，12）2.7對數(shù)與對數(shù)函數(shù)2.7對數(shù)與對數(shù)函數(shù)1.對數(shù)的概念(1)對數(shù)的定義如果ax=N(a>0且a≠1)，那么數(shù)x叫做以a為底N的對數(shù),記作_________,其中____叫做對數(shù)的底數(shù),____叫做真數(shù).Nx=logaNa對數(shù)形式特點(diǎn)記法一般對數(shù)底數(shù)為a(a>0且a≠1)_______常用對數(shù)底數(shù)為__________自然對數(shù)底數(shù)為__________lnNlgNlogaN(2)幾種常見對數(shù)10e憶一憶知識要點(diǎn)1.對數(shù)的概念(1)對數(shù)的定義Nx=logaNa對數(shù)形式特2.對數(shù)的性質(zhì)與運(yùn)算法則(1)對數(shù)的性質(zhì)①負(fù)數(shù)和零沒有對數(shù);②logaa

=1；③loga1=0.憶一憶知識要點(diǎn)(2)積、商、冪的對數(shù)運(yùn)算法則：(a>0,且a

1,M>0,N>0)2.對數(shù)的性質(zhì)與運(yùn)算法則(1)對數(shù)的性質(zhì)①負(fù)數(shù)和零沒有對數(shù)2.對數(shù)的性質(zhì)與運(yùn)算法則(3)對數(shù)的重要公式1)對數(shù)的換底公式3)四個(gè)重要推論憶一憶知識要點(diǎn)2)對數(shù)恒等式2.對數(shù)的性質(zhì)與運(yùn)算法則(3)對數(shù)的重要公式1)對數(shù)的換函數(shù)y=logax(a＞0且a≠1)圖象定義域值域單調(diào)性過定點(diǎn)趨勢取值范圍(0,+∞)R增函數(shù)(1，0)底數(shù)越大，圖象越靠近x軸0<x<1時(shí),y<0x>1時(shí),y>00<x<1時(shí),y>0x>1時(shí),y<0底數(shù)越小，圖象越靠近x軸(1，0)減函數(shù)R(0,+∞)3.對數(shù)函數(shù)圖象與性質(zhì)函數(shù)y=logax(a＞0且a≠1指數(shù)函數(shù)y=ax與對數(shù)函數(shù)_________互為反函數(shù),它們的圖象關(guān)于直線_________對稱.y=logaxy=x4.反函數(shù)5.第一象限中,對數(shù)函數(shù)底數(shù)與圖象的關(guān)系圖象從左到右,底數(shù)逐漸變大.憶一憶知識要點(diǎn)指數(shù)函數(shù)y=ax與對數(shù)函數(shù)_________互為反函練習(xí)題練習(xí)題對數(shù)與對數(shù)函數(shù)課件對數(shù)與對數(shù)函數(shù)課件6.已知函數(shù)f(x)＝|lgx|.若a≠b，且f(a)＝f(b)，則a＋b的取值范圍是()A．(1，＋∞) B．[1，＋∞)C．(2，＋∞) D．[2，＋∞)6.已知函數(shù)f(x)＝|lgx|.若a≠b，且f(a)＝f(對數(shù)與對數(shù)函數(shù)課件對數(shù)與對數(shù)函數(shù)課件(4)命題等價(jià)于x2－2ax＋3>0的解集為{x|x<1或x>3}∴x2－2ax＋3＝0的兩根為1和3，∴2a＝1＋3即a＝2(4)命題等價(jià)于x2－2ax＋3>0的解集為{x|x<1或x對數(shù)與對數(shù)函數(shù)課件9.已知函數(shù)f(x)＝loga(x＋1)(a>1),若函數(shù)y＝g(x)圖象上任意一點(diǎn)P關(guān)于原點(diǎn)對稱的點(diǎn)Q的軌跡恰好是函數(shù)f(x)的圖象.(1)寫出函數(shù)g(x)的解析式；(2)當(dāng)x∈[0,1)時(shí)總有f(x)＋g(x)≥m成立,求m的取值范圍.9.已知函數(shù)f(x)＝loga(x＋1)(a>1),若函數(shù)本題的求解體現(xiàn)了方程思想和函數(shù)思想的應(yīng)用,主要涉及對數(shù)式的求值，對數(shù)函數(shù)的圖象和性質(zhì)的綜合運(yùn)用以及與其他知識的結(jié)合(如不等式、指數(shù)函數(shù)等)．本題的求解體現(xiàn)了方程思想和函數(shù)思想的應(yīng)用,主9.已知函數(shù)f(x)＝loga(x＋1)(a>1),若函數(shù)y＝g(x)圖象上任意一點(diǎn)P關(guān)于原點(diǎn)對稱的點(diǎn)Q的軌跡恰好是函數(shù)f