分析:①根據(jù)指數(shù)函數(shù)y=3
x是增函數(shù),可知結(jié)論錯;②利用對數(shù)的換底公式log
x3=
,log
y3=
和對數(shù)函數(shù)的單調(diào)性可知,②錯;③根據(jù)對數(shù)函數(shù)y=log
4x在(0,+∞)上單調(diào)遞增,可知結(jié)論正確;④根據(jù)指數(shù)函數(shù)y=
()x是減函數(shù),可知結(jié)論錯.從而得到答案.
解答:解:∵0<x<y<1,
∴①根據(jù)指數(shù)函數(shù)y=3
x是增函數(shù),可知3
y>3
x;故①不正確;
②∵log
x3=
,log
y3=
,根據(jù)對數(shù)函數(shù)y=log
3x在(0,+∞)上單調(diào)遞增,得log
3x<log
3y<0,
∴
>,即log
x3>log
y3,故②錯;
③根據(jù)對數(shù)函數(shù)y=log
4x在(0,+∞)上單調(diào)遞增,log
4x<log
4y;故正確;
④根據(jù)指數(shù)函數(shù)y=
()x是減函數(shù),得
()x>()y,故④錯,
故答案③
點(diǎn)評:此題是個基礎(chǔ)題.考查對數(shù)函數(shù)和指數(shù)函數(shù)的單調(diào)性,并利用單調(diào)性比較大小,考查學(xué)生靈活應(yīng)用知識分析解決問題的能力.