Question

下列不等式成立的是（　　）

A．log_0.30.6＞1

B．log₃2＜0

C．0.7³＞0.6³

D．log_0.52＜log_0.53

Answer 1

分析：由對(duì)數(shù)函數(shù)y=log_0.3x，y=log_0.5x在（0，+∞）單調(diào)遞減，y=log₃x在（0，+∞）單調(diào)遞增可判斷選項(xiàng)A，B，D，由冪函數(shù)y=x³的單調(diào)遞增可判斷C

解答：解：由對(duì)數(shù)函數(shù)y=log_0.3x，y=log_0.5x在（0，+∞）單調(diào)遞減，y=log₃x在（0，+∞）單調(diào)遞增可知，
log_0.30.6＜log_0.30.3=1，故A錯(cuò)誤，
loog₃2＞log₃1=0故B錯(cuò)誤
Log_0.52＞log_0.53，故D錯(cuò)誤
由冪函數(shù)y=x³的單調(diào)遞增可知，0.7³＞0.6³，故C正確
故選C

點(diǎn)評(píng)：本題主要考查了利用對(duì)數(shù)函數(shù)與冪函數(shù)的單調(diào)性比較式子的大小，屬于基礎(chǔ)試題