The general rule is that for every and , for the functions , and , we have and . So you answer is correct except for the place of .
By the way, did you realize that for , (the order of the Earth's mass in kilograms), while (decimal logarithm)?
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.