對(duì)數(shù)函數(shù)及其性質(zhì)(講義)

1、對(duì)數(shù)函數(shù)及其性質(zhì)(講義)知識(shí)點(diǎn)睛一、對(duì)數(shù)函數(shù)的定義一般地，函數(shù)()叫做對(duì)數(shù)函數(shù)，其中X是自變量,函數(shù)的定義域是(0, +8).二、對(duì)數(shù)函數(shù)的圖象和性質(zhì)1 .對(duì)數(shù)函數(shù)y = log.x (0,且在1)的圖象和性質(zhì):2.對(duì)數(shù)函數(shù)底數(shù)變化與圖象分布規(guī)律 y = log. x , y = log/, x, y = logt. x, y = log. x,則有 OQv/vlvkc,即：xe(, +8)時(shí),logfl X logb X logcx log/, X logr x logrf x .3.反函數(shù)y = log. x與，=戈互為反函數(shù)，其中a0,且厚1；互為反函數(shù)的兩個(gè)函數(shù) 的圖象關(guān)于直線對(duì)稱.精

2、講精練1 .直接寫出下列函數(shù)的定義域：(1) y = log3(x-2)(2) y = Jog? x y = logo.s(3x-2) (4) y =!+ “一/ ln(x + l)2 .(1)已知/(x)的定義域?yàn)?, 1,則函數(shù))，= /(log|(3-x)的定義域是(2)已知函數(shù)/(x) = log1(2-log2x)的值域是(-8, 0),則它的定義域是(3)函數(shù)/(x) = log(x2+6x+13)的值域是3 .已知0,且存1,則函數(shù)y =/與y = loga(-x)的圖象只可能是()A.B.C.D.4 .函數(shù)/(x)=l + log2X與g(x)=21在同一直角坐標(biāo)系中的圖象可能

3、是()7A.B.C.D.5 .若點(diǎn)(，與在函數(shù)3Tgx的圖象上，則下列點(diǎn)也在此圖象上的是()A. (-, Z?)B. (IO。，1-Z?)C. (W, Z? + l)D. (“2, 2b)a6 .若log.2018 .已知函數(shù)/(x)= J ,若/(4)= 一，則 4=.21xWO29 .(1)已知函數(shù)y = bgg_DX在(0, +8)上為增函數(shù)，則的取值范圍是(2)已知函數(shù))，=108式2次)在(-1,1)上是天的減函數(shù)，則。的取值范圍是(3)若函數(shù)y = -log2, -ox-a)在區(qū)間(v, 1 -0)上是增函數(shù),則。的取 值范圍是.10 . (1)函數(shù)/(x)=llogxl (0且的

4、單調(diào)遞增區(qū)間是：(2)函數(shù)/(A)= logl(x2+2x)的單調(diào)遞增區(qū)間是,單調(diào)遞減區(qū)間一是;(3)已知ta)= / + 2x, g(x) = logX,則函數(shù)y = /(g(x)的單調(diào)遞增區(qū)間 2是，單調(diào)遞減區(qū)間是.11 .比較下列各組數(shù)的大?。?6(1) log! - , log, - ；(2) Iog32 , log52；5 5亍7(3) log0? 2 , log, 3 ；(4) 5，, 0.45 , log04 5 .12 .設(shè)a = log37T, b = log2 /3, c = log3/5 則()A. abc B. acb C. bac D. bca7D. bac(4) (

5、-l,0)U(0,2|13 .設(shè) a, b, c 均為正數(shù)，且2=loga, (!)” 22(-)c =log2c,則()2A. abc B. cba C. ca知識(shí)點(diǎn)睛一、對(duì)數(shù)函數(shù)的定義y = log/ (a 0,且。W 1)精講精練21. (1) (2, + s) ； (2) (0, + s) ； (3) (一，1；2. (1) 2,|； (2) (0,2) ； (3) (-oo,-23. B4. C5. D6. B71 T 27. 一或一2718. 也或T9. (1) (2,+oo) ； (2) (1, 2)； (3) 2-2x/3,210. (1) (1,+s)(2) (s, 2), (0, + s)(3) (2, + s), (0,2)46IL (1) log1 -log1 -535 /(2) log32log52(3) log032 0,45 log04512. A13. A對(duì)數(shù)函數(shù)及其性質(zhì)(隨堂測試)1 .已知函數(shù)/(x) = -4=的定義域?yàn)镸, g(x)