Question

Y=x^x^x....... Infinite times . Find x in terms of y.

Answer 1

Given that

Y = $x^{x^{x^{x^{...}}}}$

Now by considering the exponential part

which is $x^{x^{x^{x^{...}}}}$

Then we can write $x^{x^{x^{x^{...}}}}$ as $x^Y$

Now the equation

Y = $x^Y$

or

$\sqrt[Y]{x^Y}$ = $\sqrt[Y]{Y}$

or x = $Y^{\frac{1}{Y}}$

Hope it helps you