# Exercise 2.5 of SICP

Exercise 2.5: Show that we can represent pairs of nonnegative integers using only numbers and arithmetic operations if we represent the pair a and b as the integer that is the product 2a 3b. Give the corresponding definitions of the procedures cons, car, and cdr.

The discrete log procedure is a cousin of discrete-log from 1.45.

(define (cons a b)
(* (expt 2 a) (expt 3 b)))

(define (car x)
(discrete-log x 2))

(define (cdr x)
(discrete-log x 3))

(define (discrete-log n base)
(if (not
(= 0 (remainder n base)))
0
(+ 1 (discrete-log (/ n base) base))))