How to solve equations of this form: $x^x = n$? How would I go about solving equations of this form:
$$
x^x = n
$$
for values of n that do not have obvious solutions through factoring, such as $27$ ($3^3$) or $256$ ($4^4$).
For instance, how would I solve for x in this equation:
$$x^x = 7$$
I am a high school student, and I haven't exactly ventured into "higher mathematics." My first thought to approaching this equation was to convert it into a logarithmic form and go from there, but this didn't yield anything useful in the end.
My apologies if this question has been asked and answered already; I haven't been able to find a concrete answer on the matter.

The solution involves a function called Lambert's W-function.  There is a Wikipedia page on it.
As Oliver says, it is not a nice neat form.  It is an entirely new function.  Its definition is $$ye^y=z, W(z)=y$$
Can you use logs to turn $x^x=n$ into $ye^y=f(n)$, for $y$ equal to some function of $x$?
