Infinite power tower equal to two

An infinite tower of exponents $x^{x^{x^{\cdot^{\cdot^{\cdot}}}}}$ converges to the value $2$. Find $x$ and give it to the nearest integer.

1 (exactly $\sqrt2\approx1.414$). The tower equals its own exponent, so if it is $2$ then $x^2=2$ and $x=\sqrt2$, which rounds to $1$.