It is given that Y = X^x. If X is known, Y will be solved. How can you solve X here if only Y is given?

Question

It is given that Y = X^x. If X is known, Y will be solved. How can you solve X here if only Y is given?

Answer 1

you could graph x^x and find what the value is at your given y

Answer 2

y = x^x

ln y = ln x e^(ln x)

W(ln y) = ln x

ln y = x ln x

ln y / W(ln y) = x

W(z) is the Lambert W Function. If f(z) = z e^z, W(f(z)) = z.

http://en.wikipedia.org/wiki/Lambert_w_f...

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EDIT:

I'm not sure of the grade level you're in, but the Lambert W Function is advanced mathematics.