The tallest tower of $x$ so far

Number Theory Level 1

$\huge x^{x^{x^{...}}} = 2$

Find the value of $x$ .

\sqrt{2}

2 \pi

4 2

\sqrt{8}

\sqrt{\frac{\pi}{2}}

2 solutions

Hana Wehbi
Nov 16, 2017

$\large x^{x^{x^{...}}} = 2 \implies x^2=2 \implies x=\sqrt{2}$

Jordan Baillie
Apr 18, 2018

Take log x of both sides.

It follows that 2=x^x^x.....

So x^2=2

x=sqrt2