EDIT: There is another question, just like this one, by "Bert van den Bosch", if you wish to see another thread with some detailed answers to this question. They may have some better explanations to the given problem.
I assume everyone here is familiar with the fact that if you take two numbers: a, and b, and multiply them, you have essentially repeated adding $a+a+a+…+a$, such that b describes the mumber of a's added together.
Most of us are also familiar with $a*a*a*…*a=a^b$ defining exponentiation.
Is there a function f(x,y) such that:
$$f(a,f(a,f(a,…f(a,a)…)))=a+b$$
or,
$$f(f(f(…f(a,a)…,a),a),a)=a+b$$
with b describing the number of a's in the equation?
