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This is the Omega constant, which satisfies each of these simple equations (all equivalent):

ex = 1/x x = ln(1/x) = - ln(x)
e-x = x -x = ln(x)
x ex = 1 x+ln(x) = 0
x1/x = 1/e x/ln(x) = -1
x-1/x = (1/x)(1/x) = e ln(x)/-x = 1

Thus it is sort of like the golden ratio. In the above equations, if e is replaced with any number bigger than 1 (and "ln" by the corresponding logarithm) and you get another "Omega" constant. For example:

if 2x=1/x, then x=0.6411857445... 
if πx=1/x, then x=0.5393434988... 
if 4x=1/x, then x=1/2 
if 10x=1/x, then x=0.3990129782... 
if 27x=1/x, then x=1/3 
if 10000000000x=1/x, then x=1/10

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