Logarithms will buy you the first three.
That is now rather easy to order.
The last to are easy enough by themselves. One is n factors of n and the other is n factors, but only the largest is as great as n.
Two logs will settle everything but the factorial. You do that.
All we've left is the factorial vs. the
No ideas? Search the brain.
Note: The log is useful because it is monotonic increasing. This is a useful transformation that does not change the order of anything.