SOLUTION: 2x^-x=1

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Question 490996: 2x^-x=1
Found 2 solutions by Alan3354, ccs2011:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Is -x the exponent of x?
2x%5E%28-x%29+=+1
x%5E%28-x%29+=+1%2F2
1%2Fx%5Ex+=+1%2F2
x%5Ex+=+2
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That can be solved using numerical methods such as successive approximation.
A power series or other series might do it, too, but I suspect this is not the problem you were given.

Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Make exponents positive
--> 2%2F%28x%5Ex%29+=+1
--> x%5Ex+=+2
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This cannot be solved explicitly using elementary operations
see wolfram alpha more explanation
http://www.wolframalpha.com/input/?i=x^x+%3D+2
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You can graph y = x^x, and see where y =2.
If you know calculus you can use Newtons method to approximate the root of f(x) = x^x - 2
Approximate solution is x = 1.5596