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x^2-2ln(x)=0 equation

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Numerical solution:

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The solution

You have entered [src] 
 2               
x  - 2*log(x) = 0
$$x^{2} - 2 \log{\left(x \right)} = 0$$
Simplify
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
                     -re(W(-1))       -re(W(-1))                
                     -----------      -----------               
        /im(W(-1))\       2                2         /im(W(-1))\
x1 = cos|---------|*e            - I*e           *sin|---------|
        \    2    /                                  \    2    /
$$x_{1} = e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \cos{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)} - i e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \sin{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)}$$ 
x1 = exp(-re(LambertW(-1))/2)*cos(im(LambertW(-1))/2) - i*exp(-re(LambertW(-1))/2)*sin(im(LambertW(-1))/2)
Sum and product of roots [src] 
sum
                -re(W(-1))       -re(W(-1))                
                -----------      -----------               
   /im(W(-1))\       2                2         /im(W(-1))\
cos|---------|*e            - I*e           *sin|---------|
   \    2    /                                  \    2    /
$$e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \cos{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)} - i e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \sin{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)}$$ 
=
                -re(W(-1))       -re(W(-1))                
                -----------      -----------               
   /im(W(-1))\       2                2         /im(W(-1))\
cos|---------|*e            - I*e           *sin|---------|
   \    2    /                                  \    2    /
$$e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \cos{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)} - i e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \sin{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)}$$ 
product
                -re(W(-1))       -re(W(-1))                
                -----------      -----------               
   /im(W(-1))\       2                2         /im(W(-1))\
cos|---------|*e            - I*e           *sin|---------|
   \    2    /                                  \    2    /
$$e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \cos{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)} - i e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \sin{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)}$$ 
=
   re(W(-1))   I*im(W(-1))
 - --------- - -----------
       2            2     
e
$$e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(-1\right)\right)}}{2}}$$ 
exp(-re(LambertW(-1))/2 - i*im(LambertW(-1))/2)
Numerical answer [src] 
x1 = 0.919969704921981 + 0.726782465920494*i
x2 = 0.91996970492198 - 0.726782465920492*i
x3 = 0.91996970492198 + 0.726782465920492*i
x4 = 0.919969704921981 + 0.726782465920494*i
x5 = 0.919969704921981 + 0.726782465920494*i
x5 = 0.919969704921981 + 0.726782465920494*i
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