# SICP Exercise 1.36

Modified fixed-point procedure:

```
(define (fixed-point f first-guess)
(define (close-enough? v1 v2)
(display "x=")
(display v1)
(display " and f(x)=")
(display v2)
(newline)
(< (abs (- v1 v2)) tolerance))
(define (try guess)
(let ((next (f guess)))
(if (close-enough? guess next)
next
(try next))))
(try first-guess))
```

Without average damping:

```
> (fixed-point (lambda (x) (/ (log 1000) (log x))) 1.1)
```

This gives us the answer in 33 iterations.

With average damping:

```
> (fixed-point (lambda (x) (average x (/ (log y) (log x)))) 10.0)
```

This gives the answer in 10 iterations.