已知a=(1⼀2)^1⼀3,b=(1⼀3)^1⼀2,c=log1⼀2^1⼀3则abc之间的大小关系为

A.a>b>cB.c>a>bC.a>c>bD.c>b>a
2025-02-11 23:23:57
推荐回答(1个)
回答1:

c明显小于0,a>b>0.
对a,b同时取对数
loga=(1/3)*log(1/2);logb=(1/2)*log(1/3);
loga=-(1/3)*log(2)<0;logb=-(1/2)*log(3)<0;
(loga)/(logb)=(2*log(2))/(3*log(3))<1;
又loga,logb<0;
所以a>b