Question

下列各式正確的題目序號有

 

．
①log₂6-log₂3=log₂3；②

lg16

lg2

=lg14；③log₃9=3；④log_0.72.1＞log_0.71.9；⑤1.5^0.3＞0.8^1.2；⑥0.9

1

2

＞0.8

1

2

．

Answer 1

分析：①②根據(jù)對數(shù)的運算性質(zhì)loga

M

N

=logaM-logaN，log_aMN=log_aM+log_aN判斷
③根據(jù)指數(shù)與對數(shù)的轉(zhuǎn)化判斷，④根據(jù)對數(shù)函數(shù)y=log_0.7x的單調(diào)性判斷，⑤根據(jù)指數(shù)函數(shù)的單調(diào)性可判斷⑥根據(jù)冪函數(shù)y=x

1

2

的性質(zhì)判斷

解答：解：①根據(jù)對數(shù)的運算性質(zhì)loga

M

N

=logaM-logaN，log_aMN=log_aM+log_aN可知①正確，②錯誤
③根據(jù)指數(shù)與對數(shù)的轉(zhuǎn)化log₃9=2，故③錯誤
④根據(jù)對數(shù)函數(shù)y=log_0.7x的單調(diào)遞減可得④錯誤
⑤根據(jù)指數(shù)函數(shù)的單調(diào)性可得1.5^0.3＞1，0.8^1.2＜1⑤正確
⑥根據(jù)冪函數(shù)y=x

1

2

的性質(zhì)可得⑥正確
故答案為：①⑤⑥

點評：本題主要考查了對數(shù)的運算性質(zhì)，指數(shù)式與對數(shù)式的轉(zhuǎn)化，對數(shù)函數(shù)的單調(diào)性，知識函數(shù)的單調(diào)性的應(yīng)用，冪函數(shù)的單調(diào)性的應(yīng)用，綜合的知識較多，此類問題要求考生具備較強的綜合能力．