Why doesn't Wolfram Alpha understand: solve (x^(x^x))=2 for x ?

Questions
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1

Why doesn’t Wolfram Alpha understand: solve (x^(x^x))=2 for x ?
For example, the equation x^x=2 has the solution x = e^W(log(2))≈1.55961.

2

If W(z) denotes the solution to z = W\;e^W, W \ge -1, then for x = e^{W(\log(2))}, x^{x^x} evaluates to 2.4... for me. So maybe W denotes something else?

Also, “solve (x^(x^x))=2 for x > 0” gives the solution x = 1.47668 on WolframAlpha, but it gives only a numerical solution:

Changing “solve” to “plot” gives a graphical illustration confirming a solution near x=1.47...:

3

What solution are you expecting?