correct ordering of asymptotic growth

Question

Hello I have solved this problem but I doubt if my answer is correct or not.

Write the following functions in a correct ordering of asymptotic growth, starting with the slowest growing.

n^2logn , n^(0.0001) , (logn)^(10000) , n(logn)^2 , 10^100 , nsqrt(n)logn , 2^n , n^(logn)

and this is my answer:

10^100 < n^(0.0001) < n(logn)^2 < nsqrt(n)logn < (logn)^(10000) < n^2logn < 2^n < n^(logn)

Is my answer correct??

Answer 1

(logn)^c grows asymptotically slower than n^d for any constants c and d>0, so (logn)^(10000) should be placed after 10^100.

n^(logn) is the same as e^((logn)^2) (or 2^((logn)^2) depending on the base you assume for log), which is (for similar reason) asymptotically dominated by 2^n.

Otherwise looks correct, although the way you wrote the terms may cause ambiguities in interpretation.