I am getting more and more familiar with the whole concept of time complexity but I have never encountered an example where more than one parameter is involved. Therefore, is it possible(well, I am sure it is :”)) and how to prove

a^n = Θ(logn)

or any other, similar-looking expression?

c1 * logn ≤ a^n ≤ c2 * logn

where, e.g. c1 = 1 and c2 = 2,

logn ≤ a^n ≤2 * logn.

Can I go one step further and set n, to be equal e.g. 2? This way I will get

log(2) ≤ a^2 ≤ log(4)

Which is surely true(for a between ~ 0.55 and 0.77)…

…but isn’t that too specific and interfere with the inequality too much? Sorry if the answer is trivial but Google is not helping and I have nobody to ask for explanation.