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2*x-ln(x)+0,5=0 equation

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Numerical solution:

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The solution

You have entered [src]
2*x - log(x) + 1/2 = 0
$$\left(2 x - \log{\left(x \right)}\right) + \frac{1}{2} = 0$$
The graph
Rapid solution [src]
         / /    1/2\\       / /    1/2\\
       re\W\-2*e   //   I*im\W\-2*e   //
x1 = - -------------- - ----------------
             2                 2        
$$x_{1} = - \frac{\operatorname{re}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2}$$
x1 = -re(LambertW(-2*exp(1/2)))/2 - i*im(LambertW(-2*exp(1/2)))/2
Sum and product of roots [src]
sum
    / /    1/2\\       / /    1/2\\
  re\W\-2*e   //   I*im\W\-2*e   //
- -------------- - ----------------
        2                 2        
$$- \frac{\operatorname{re}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2}$$
=
    / /    1/2\\       / /    1/2\\
  re\W\-2*e   //   I*im\W\-2*e   //
- -------------- - ----------------
        2                 2        
$$- \frac{\operatorname{re}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2}$$
product
    / /    1/2\\       / /    1/2\\
  re\W\-2*e   //   I*im\W\-2*e   //
- -------------- - ----------------
        2                 2        
$$- \frac{\operatorname{re}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2}$$
=
    / /    1/2\\       / /    1/2\\
  re\W\-2*e   //   I*im\W\-2*e   //
- -------------- - ----------------
        2                 2        
$$- \frac{\operatorname{re}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2}$$
-re(LambertW(-2*exp(1/2)))/2 - i*im(LambertW(-2*exp(1/2)))/2
Numerical answer [src]
x1 = -0.268160645457627 + 0.9262953167672*i
x1 = -0.268160645457627 + 0.9262953167672*i