algorithm - Compute size N that can be solved in certain amount of time -

i working on exercise (note no homework question) number of steps can exercised computer given , 1 asked compute n in relation time intervals multiple functions functions.

i have no problem doing functions such f(n) = n, n^2, n^3 , like.

but when comes f(n) = lgn, sqrt(n), n log n, 2^n, , n! run problems.

it clear me i have construct term of form func(n) = interval , have n.

but how functions above?

can please give me example, or name inverse functions can on wikipedia or somewhere else.

your question isn't algorithms, or complexity, inversions of math formulas.

it's easy solve n in n^k = n in closed form. unfortunately, other functions either not known or known not possible. in particular, n log(n), solution involves lambert function, doesn't much.

in cases, have solve kind of stuff numerically.