Quandaries and Queries


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 xxx...=2. So assume such a number exists, then

2 = xxx...

Now find x2. Since 2 is xxx..., x2 is xxx... = 2.

So what is x?



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