Take a variable * x *and raise it to the

**x**^{th}power:

*; call the result*

**x**^{x}*.*

**y**Now raise

*to the*

**x***power:*

**y***; call that result*

**x**^{y}*. i.e. replace the previous value of*

**y****with the value of**

*y**.*

**x**^{y}Again, raise

*to the*

**x***power:*

**y***; and replace the previous value of*

**x**^{y}**with the value of**

*y**.*

**x**^{y}Repeat this an arbitrarily large number of times, and set the result equal to 2.

That creates the infinite exponential sequence

*to the*

**x***to the*

**x***to the*

**x***to the*

**x***to the*

**x***.... =*

**x****2**.

What value of

*, if any, satisfies the equation?*

**x**