Is there any function with a rate of growth between $n$ and $\log(n)$?
My problem is that I have a value $x$, against which a term varies. The term does not vary as rapidly a linear function of $x$ but not as slowly as $log(x)$ (Choosing a different base of log can't help as for larger n the change in the function will still only happen for an large (exponential) increase).
How to model that function $f(x)$?
Best Answer
$\log{n}$ grows more slowly than any positive power of $n$, so $n^{1/2}$, $n^{2/3}$, $n^{1/\pi}$ are all possibilities. You really need a more concrete idea of the growth to work out which applies.