I'm following through the Structure and Interpretation of Computer Programs, and in an example, they talk about finding fixed points of function (where $f(x) = x$)
They then go on to say, if we want to find what x would be, where $x^x = 1000$
We can find that by finding the fixed point of $f(x) = \frac{log(1000)}{log(x}$
I have a feeling that it's right, but would have trouble coming up with that answer on my own.
How do you go from knowing $x^x = 1000$, to figuring out that it's the fixed point of $f(x) = \frac{log(1000)}{log(x}$
$\displaystyle x^x = 1000 \implies log(x^x) = log(1000) \implies xlog(x) = log(1000) \implies x = \frac{log(1000)}{log(x)}$
So if $f(x) = \frac{log(1000)}{log(x)}$, we're looking for $f(x) = x$.