What Does e^ln|x| Equal: x or |x|?

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If I take e^ln|x|, do I get x or |x|?
 
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|x|

For example, if x = -1, ln(x) is undefined, but ln|x| = 0, and e^ln|x| = e^0 = 1 = |-1|
 
e(any real number) is always positive.
 

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Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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