高一数学-对数函数-比较大小问题

Question

第六题
看不清的是log a底3和log b底3

Answer 1

答案没错就是C，b>a>1比如b=9,a=3,log(a,3)=1,log(b,3)=1/2

log(a,3)>log(b,3)>0,{log(a,3)>0,log(a,3)=log(3,3)/log(3,a)=1/log(3,a)>0,a>1;同理b>1}
log(a,3)-log(b,3)>0,
log(10,3)-log(10,a)-[log(10,3)-log(10,b)]>0
log(10,b)-log(10,a)>0
log(10,b/a)>0
b/a>1,
b>a>1追问

我们数学老师给的答案是A- -、求解。。

追答

log(10,3)/log(10,a)-[log(10,3)/log(10,b)]>0
[log(10,b)-log(10,a)]log(10,3)/[log(10,b)*log(10,a)]>0
log(10,b/a)log(10,3)/[[log(10,b)*log(10,a)]>0,{a,b>1,log(10,a)>0,log(10,b)>0,log(10,3)>0}
log(10,b/a)>0
b/a>1,
b>a>1