#1**+2 **

2^x = x^2 take the log of each side

log 2^x = log x^2 and we can write

x log 2 = 2 log x

Rearrange as

x / log x = 2 / log 2

And it must be that x = 2

CPhill Oct 27, 2019

#2**+3 **

Apparently 4 is a possible solution as well, according to WolframAlpha. However, I have no idea how to solve it.

ThatOnePerson Oct 27, 2019