Question

比較a，b，c的大小，其中a=0.2²，b=2^0.2，c=log_0.22（ ）
A．b＞c＞a
B．c＞a＞b
C．a(chǎn)＞b＞c
D．b＞a＞c

Answer 1

【答案】分析：將log_0.22看作函數(shù)y=log_0.2x當(dāng)x=2時(shí)所對(duì)應(yīng)的函數(shù)值小于零，將a=0.2²看作函數(shù)y=0.2^x當(dāng)x=2時(shí)所對(duì)應(yīng)的函數(shù)值小于1，將b=2^0.2看作函數(shù)y=2^x當(dāng)x=0.2時(shí)所對(duì)應(yīng)的函數(shù)值大于1．
解答：解：根據(jù)對(duì)數(shù)函數(shù)的性質(zhì)可知c=log_0.22＜0
根據(jù)指數(shù)函數(shù)的性質(zhì)可知0＜0.2²＜1，2^0.2＞1
∴b＞a＞c
故選D
點(diǎn)評(píng)：本題主要考查在數(shù)的比較中，我們要注意函數(shù)思想的應(yīng)用．