Your task in this exercise is to put the following functions into their appropriate positions in the list so that finally the list will contain all the functions in ascending order of their growth rates. You can swap two functions by clicking on them.
Constant terms never matter, so ignore something like multiplying by 9.
Focus on the exponent.
Generally, things that are only logs go first.
Note that \log \log n (taking the log of
\log n) grows slower than
\log^2 n (multiplying \log n by itself).
Generally, constant powers of n come after
things with only log factors.
Even a small constant power of n grows
faster than things with only
logs. So \sqrt{n} grows faster
than \log^3 n.
Generally, things with some function of n
in the exponent go last. These are called "exponentials".
Of the exponentials, just see what has the biggest
function in the exponent. For example,
since \sqrt{n} grows faster than
\log n, then 2^\sqrt{n} grows faster
than 2^{\log n}.