How to output letter case relations based on size relations?

Questions
1

{a, b, c} = {Log[2, Sqrt[3]], Log[4, Sqrt[6]], Log[6, 3]}
Sort[%, Greater]

Based on the above code, we can obtain the size relationships of the three numerical values, which are assigned to the letters a, b, and c. How can we manipulate them so that the final result is in the form

a > b > c?

2

Perhaps NumericalSort[list]? Or Reverse@NumericalSort[list].

3

Here is a way:

Clear[a, b, c];
numbers = {Log[2, Sqrt[3]], Log[4, Sqrt[6]], Log[6, 3]};
letters = {a, b, c};
Inactive[Greater] @@ Sort[numbers, Greater] /.
  Thread[numbers -> letters] // Activate
4

In the end, it’s not the three numerical values that are displayed in order, but the assigned letters corresponding to the three values that are sorted, i.e., a > b > c.

5

Perfect! Exactly what I needed.

6

Perhaps it wasn’t clear what you meant. I thought something like the following:

{a, b, c} = Reverse@NumericalSort@{Log[2, Sqrt[3]], Log[4, Sqrt[6]], Log[6, 3]};
a > b > c
(*  True  *)