Question

已知m=0.9^5.1,n=5.1^0.9,p=log_0.95.1,則這三個(gè)數(shù)的大小關(guān)系是(    )

A.m＜n＜p                             B.m＜p＜n

C.p＜m＜n                             D.p＜n＜m

Answer 1

思路解析:本題考查指數(shù)函數(shù)的單調(diào)性和對(duì)數(shù)函數(shù)的單調(diào)性.

由指數(shù)函數(shù)的性質(zhì),∵0＜0.9＜1,5.1＞1,

∴0＜0.9^5.1＜1,即0＜m＜1.

又∵5.1＞1,0.9＞0,

∴5.1^0.9＞1,即n＞1.

由對(duì)數(shù)函數(shù)的性質(zhì),∵0＜0.9＜1,5.1＞1,

∴l(xiāng)og₀.₉5.1＜0,即p＜0.

綜合可得p＜m＜n.

答案:C