x in degree x

We have the equation:
X to the power of X to the power of X to the power of ... etc. equals 2

It is necessary to find the value of X.

Without falling into a stupor, but after thinking a little, we realize: in order to raise X to a power, it would be nice to know this power. Peering carefully at equation (1), we notice that the exponent is: 

Again this endless expression... But after all (according to the problem statement) it is equal to 2​. Thus, equation (1) can be rewritten in a simpler way: 

Now the solution is obvious: take the square root and get (we'll limit ourselves to 9 signs) 😁 

Bingo ! We got it!

But suddenly ...
a clever man appears and said:

- Let's solve this : 

It is very similar to equation (1), only difference is: there is number four '4' instead of two '2'. Reasoning, as before, we write down: 

Wow! Confusion! 😒 

Ok, the solution for equation(1) is confirmed.

But what to do with equation (3) ???