Use the rules and definition for ordering Θ-classes to arrange the following in order from lowest to highest:

lg n ; (lg n)^6 ; lg(n^n) ; n^4 ; n^(1/2) ; 5n^3+n^2 ; 1^n ; (1.001)^n ; 5^n

I used the rules as I understood them and ended very uncertainly with the following order:

1^n (1 to the power of anything is)

lg n

n^(1/2)

lg (n^n)

5n^3+n^2

n^4

(lg n)^6

(1.001)^n

5^n

I'm really not sure about the order so if someone could please check and tell me where and why I went wrong I would really appreciate it.

Thanks in advance.