# If x^x^x^x^x...=2 then what is x? If x^x^x^x^x...=2 then what is x, please share your working also.

2
by sinderniavanshi

2015-11-11T06:18:23+05:30

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X^x^x^.... = 2 = y
This can be written as x^y. Even if we remove 1 x what remains is the same.
x^2 = 2 -> x = √2

2015-11-11T06:55:48+05:30

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X^x^x^x^x... = 2
Let x^x^x^x^x... = 2 = z

x^z = x^(x^x^x^x^x...) = x^x^x^x^x^x... = 2
⇒ x^2 = 2
⇒ x = √2