#
Fixed point
^{
}

Modify
`fixed-point`

so that it prints the sequence of approximations it generates, using the
`newline`

and
`display`

primitives shown in exercise
1.22
. Then find a solution to
`x^x = 1000`

by finding a fixed point of
`x → log(1000)/log(x)`

. (Use Scheme's primitive
`log`

procedure, which computes natural logarithms.) Compare the number of steps this takes with and without average damping. (Note that you cannot start
`fixed-point`

with a guess of 1, as this would cause division by
`log(1) = 0`

.)

```
(check-equal? (round (* 100 (fixed-point cos 1.0))) 74)
(check-equal? (round (* 100 (fixed-point (lambda (y) (+ (sin y) (cos y))) 1.0))) 126)
```