Question

下列式子中成立的是

1. A.
   log_0.44＜log_0.46
2. B.
   1.01^3.4＞1.01^3.5
3. C.
   3.5^0.3＜3.4^0.3
4. D.
   log₇6＜log₆7

Answer 1

D
分析：分別構(gòu)造函數(shù)，根據(jù)函數(shù)的性質(zhì)，比較每組函數(shù)值的大小
解答：對于A：設(shè)函數(shù)y=log_0.4x，則此函數(shù)單調(diào)遞減∴l(xiāng)og_0.44＞log_0.46∴A選項(xiàng)不成立
對于B：設(shè)函數(shù)y=1.01^x，則此函數(shù)單調(diào)遞增∴1.01^3.4＜1.01^3.5 ∴B選項(xiàng)不成立
對于C：設(shè)函數(shù)y=x^0.3，則此函數(shù)單調(diào)遞增∴3.5^0.3＞3.4^0.3 ∴C選項(xiàng)不成立
對于D：設(shè)函數(shù)f（x）=log₇x，g（x）=log₆x，則這兩個(gè)函數(shù)都單調(diào)遞增∴l(xiāng)og₇6＜log₇7=1＜log₆7∴D選項(xiàng)成立
故選D
點(diǎn)評(píng)：本題以比較大小的形式考查指數(shù)函數(shù)和冪函數(shù)的性質(zhì)，要求對指數(shù)函數(shù)和冪函數(shù)的單調(diào)性熟練掌握．屬簡單題