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x^(log(x))=10

x^(log(x))=10 equation

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Numerical solution:

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The solution

You have entered [src] 
 log(x)     
x       = 10
xlog⁡(x)=10x^{\log{\left(x \right)}} = 10
Simplify
The graph
-7.5-5.0-2.50.02.55.07.510.012.515.017.520.001000000000000000000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
         _________
      -\/ log(10) 
x1 = e
x1=e−log⁡(10)x_{1} = e^{- \sqrt{\log{\left(10 \right)}}} 
        _________
      \/ log(10) 
x2 = e
x2=elog⁡(10)x_{2} = e^{\sqrt{\log{\left(10 \right)}}} 
x2 = exp(sqrt(log(10)))
Sum and product of roots [src] 
sum
    _________      _________
 -\/ log(10)     \/ log(10) 
e             + e
e−log⁡(10)+elog⁡(10)e^{- \sqrt{\log{\left(10 \right)}}} + e^{\sqrt{\log{\left(10 \right)}}} 
=
   _________       _________
 \/ log(10)     -\/ log(10) 
e            + e
e−log⁡(10)+elog⁡(10)e^{- \sqrt{\log{\left(10 \right)}}} + e^{\sqrt{\log{\left(10 \right)}}} 
product
    _________    _________
 -\/ log(10)   \/ log(10) 
e            *e
elog⁡(10)elog⁡(10)\frac{e^{\sqrt{\log{\left(10 \right)}}}}{e^{\sqrt{\log{\left(10 \right)}}}} 
=
1
11 
1
Numerical answer [src] 
x1 = -25.2915347925395 + 6.54085266249859*i
x2 = -25.2915347925395 - 6.54085266249859*i
x3 = 4.56047657161819
x4 = 4.5604765716182
x4 = 4.5604765716182
The graph
x^(log(x))=10 equation
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