1.函數(shù)y=logax的圖象如圖所示,則實(shí)數(shù)a的可能取值為( )
A.5 B. C. D.
A [由圖可知,a>1,故選A.]
2.若對(duì)數(shù)函數(shù)過(guò)點(diǎn)(4,2),則其解析式為_(kāi)_______.
f(x)=log2x [設(shè)對(duì)數(shù)函數(shù)的解析式為f(x)=logax(a>0且a≠1).由f(4)=2得loga4=2,∴a=2,即f(x)=log2x.]
3.函數(shù)f(x)=log2(x+1)的定義域?yàn)開(kāi)_______.
(-1,+∞) [由x+1>0得x>-1,故f(x)的定義域?yàn)?-1,+∞).]
對(duì)數(shù)函數(shù)的概念及應(yīng)用
【例1】 (1)下列給出的函數(shù):①y=log5x+1;
②y=logax2(a>0,且a≠1);③y=log(-1)x;
④y=log3x;⑤y=logx(x>0,且x≠1);
⑥y=logx.其中是對(duì)數(shù)函數(shù)的為( )
A.③④⑤ B.②④⑥
C.①③⑤⑥ D.③⑥
(2)若函數(shù)y=log(2a-1)x+(a2-5a+4)是對(duì)數(shù)函數(shù),則a=________.
(3)已知對(duì)數(shù)函數(shù)的圖象過(guò)點(diǎn)(16,4),則f=__________.