How would you go about solving an equation like this, and what values of x did you end up with.

$$x=2^{\frac 1x}$$

Also, how would you generalise for

$$x=n^{\frac1x}$$

These come from

$$\sqrt[{\sqrt[{\sqrt[\cdots]n}]n}]n$$
$$x=\sqrt[{\sqrt[{\sqrt[\cdots]n}]n}]n$$
$$x=\sqrt[x]n$$
$$x=n^{\frac1x}$$