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It's not a proof, but a start.

Hmm. It's obvious that once it gets to 2 then it will stay there because (√2)² = 2, but that's not anywhere close to a proof.

yes, its very interesting. As you add up more "^x" terms, the solution get closer to SQRT(2).Again, I would like to see a demonstration of this (or a counter example): )

Well then, you should exponentiate in this order I believe:x^(x^(x^(x^x)))In Excel (by trial and error) I get: 1.432694...

That's exactly how it was written.

x^x^x^x^x=2x ≈ 1.425385621 ≈ √2I think the solution of x^x^x^...........=2 converges into √2.If someone proved that it would be remarkable.

Is that (((x^x)^x)^x)^x or x^(x^(x^(x^x)))?I'm just asking that to stall for time, because I have no idea how to start trying to solve it. Probably using logs.

Someone showed me this problem today and I couldn't think of how to solve it:x^x^x^x^x = 2Anyone know how to solve it and if so can you explain how you get to your answer?