Logarithmic Recursion

Exercise 4.3 has you compute the actual number of multiplications done by the third version of mod-expt given an exponent.
     > (mod-expt-mults signing-exponent)
     984
The dramatic speedup is due to the fact that at each step mod-expt divides the exponent in half.

Q: If e is the exponent, then how is the number of multiplications expressed in big-Theta notation?

A: Θ(log e) instead of Θ(e)

mod-expt is now an example of logarithmic recursion (instead of linear recursion).

Q: How is the amount of memory required by mod-expt expressed in big-Theta notation?