#lang sicp

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

(define (car pair)
  (if (= (remainder pair 3) 0)
      (car (/ pair 3))
      (log2 pair)))

(define (cdr pair)
  (if (= (remainder pair 2) 0)
      (cdr (/ pair 2))
      (log3 pair)))

(define (log2 num)
  (define (aux num acc)
    (if (<= num 1)
        acc
        (aux (/ num 2) (+ acc 1))))
  (aux num 0))

(define (log3 num)
  (define (aux num acc)
    (if (<= num 1)
        acc
        (aux (/ num 3) (+ acc 1))))
  (aux num 0))