关于sicp书中 1.36的问题

Question

第一次读题的时候，把题目中给的表达式看错成了
log(1000 / log(x))，然后发现采用平均阻尼的步数比不用平均阻尼更多。想问一下应该怎么证明这个情况。然后在什么时候会发生这种情况。谢谢

(define tolerance 0.00001)

(define (fixed-point f first-guess)
    (define (close-enough? v1 v2)
        (< (abs (- v1 v2)) tolerance))
    (define (try guess)
        (display guess)
        (display #\newline)
        (let ((next (f guess)))
            (if (close-enough? guess next)
                next
                (try next))))
    (try first-guess))

(define (abs x)
    (if (< x 0)
        -x
        x))

(fixed-point (lambda (x) (log (/ 1000 (log x)))) 2)
(display #\newline)
(fixed-point (lambda (x) (/ (+ x (log (/ 1000 (log x))))2)) )
(exit)