Question

2．四個(gè)數(shù)2.4^0.8，3.6^0.8，log_0.34.2，log_0.40.5的大小關(guān)系為（　�。�

• A． 3.6^0.8＞log_0.40.5＞2.4^0.8_＞log_0.34.2
• B． 3.6^0.8＞2.4^0.8_＞log_0.34.2＞log_0.40.5
• C． log_0.40.5＞2.4^0.8_＞3.6^0.8log_0.34.2
• D． 3.6^0.8＞2.4^0.8_＞log_0.40.5＞log_0.34.2

Answer 1

分析 由對(duì)數(shù)函數(shù)的性質(zhì)判出1＞log_0.40.5＞log_0.34.2，由指數(shù)函數(shù)的性質(zhì)得到3.6^0.8＞2.4^0.8＞1．，則四個(gè)數(shù)的大小得到比較．

解答 解：∵由對(duì)數(shù)函數(shù)圖象可得：1=${log}_{0.4}^{0.4}$${＞log}_{0.4}^{0.5}$＞0＞${log}_{0.3}^{4.2}$，
又∵利用指數(shù)函數(shù)圖象可得：3.6^0.8＞2.4^0.8＞1．
∴3.6^0.8＞2.4^0.8＞log_0.40.5＞log_0.34.2．
故選：

點(diǎn)評(píng) 本題考查了不等關(guān)系與不等式，考查了指數(shù)函數(shù)、對(duì)數(shù)函數(shù)的圖象和性質(zhì)，屬于基礎(chǔ)題．