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x^(log(x))=10000 equation

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Numerical solution:

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The solution

You have entered [src] 
 log(x)        
x       = 10000
xlog⁡(x)=10000x^{\log{\left(x \right)}} = 10000
Simplify
The graph
152025303540450200000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
           _________
      -2*\/ log(10) 
x1 = e
x1=e−2log⁡(10)x_{1} = e^{- 2 \sqrt{\log{\left(10 \right)}}} 
          _________
      2*\/ log(10) 
x2 = e
x2=e2log⁡(10)x_{2} = e^{2 \sqrt{\log{\left(10 \right)}}} 
x2 = exp(2*sqrt(log(10)))
Sum and product of roots [src] 
sum
      _________        _________
 -2*\/ log(10)     2*\/ log(10) 
e               + e
e−2log⁡(10)+e2log⁡(10)e^{- 2 \sqrt{\log{\left(10 \right)}}} + e^{2 \sqrt{\log{\left(10 \right)}}} 
=
      _________        _________
 -2*\/ log(10)     2*\/ log(10) 
e               + e
e−2log⁡(10)+e2log⁡(10)e^{- 2 \sqrt{\log{\left(10 \right)}}} + e^{2 \sqrt{\log{\left(10 \right)}}} 
product
      _________      _________
 -2*\/ log(10)   2*\/ log(10) 
e              *e
e2log⁡(10)e2log⁡(10)\frac{e^{2 \sqrt{\log{\left(10 \right)}}}}{e^{2 \sqrt{\log{\left(10 \right)}}}} 
=
1
11 
1
Numerical answer [src] 
x1 = -68.3921524667838 - 12.3568387326607*i
x2 = 20.7979465602784
x3 = -68.3921524667838 + 12.3568387326607*i
x3 = -68.3921524667838 + 12.3568387326607*i
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