Single Variable in Multiple Places Exponent/Logarithm

Question

How on Earth do I solve for $x$ when: $2 = x^{x-1}$ ? I know that the obvious solution is $2$, & that the other is approximately $.346323362$, but want an exact way to write it, i.e. $\ln(2)/2$ or something like that. I have scoured the internet & have found nothing helpful so far.