How to approximate a f(t) in terms of t when f(t) is a function of itself?

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So I have a function

$f(x)=\left\{ \begin{array}{lr} 1, & x = 0 \\ 3 + f(x/2), & x = even \\ 3 + f((x-1)/2), & x = odd \end{array} \right.$

and I can see from graphing it, that it is approximately:

$f(x)=3\log_{2}(x) + 4$

where x > 0

what method(s) can I use to find this solution? Some kind of correlation? or is there an algebraic solution? or something else?

Problem source, incase I missed something: https://www.youtube.com/watch?v=Ud3oeInn_8c