My name is Ryan

level if question is 10-12th grade my Teacher is asking this question
 
ok the question is you have a number say x and it is to the power of x which is to the power of x and so on infinite times   like   x^x^x^x^x^x^x^...  i have to figure out what x is so that the answer is always 2 i came up with two ideas but neither of them seem to work.

Hi Ryan,

First you need to assume that there is some number x so that x^xx...=2. So assume such a number exists, then

2 = x^xx...

Now find x². Since 2 is x^xx..., x² is x^xx... = 2.

So what is x?

Penny

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