These are the functions that I have:
$$\log n, (\log n)^2, \ln(m), n^\frac{1}3+\log n, \sqrt{n}, \frac{n}{\log n},( \frac{3}2)^n $$
From what I understand, this is what I come up from the lowest to highest growth rate.
$$\log n < (\log n)^2 < \ln(m)< n^\frac{1}3+\log n < \sqrt{n} < \frac{n}{\log n} <( \frac{3}2)^n $$
But I am not sure this is correct, is there anyone could help to explain how to solve these ? Putting in number as examples definitely helps.
Thank You!