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log(x-log(0.5*x)-2)^(41/2)=0 equation

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Numerical solution:

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The solution

You have entered [src]
   41/2/       /x\    \    
log    |x - log|-| - 2| = 0
       \       \2/    /    
$$\log{\left(\left(x - \log{\left(\frac{x}{2} \right)}\right) - 2 \right)}^{\frac{41}{2}} = 0$$
The graph
Sum and product of roots [src]
sum
  /    -3\
-W\-2*e  /
$$- W\left(- \frac{2}{e^{3}}\right)$$
=
  /    -3\
-W\-2*e  /
$$- W\left(- \frac{2}{e^{3}}\right)$$
product
  /    -3\
-W\-2*e  /
$$- W\left(- \frac{2}{e^{3}}\right)$$
=
  /    -3\
-W\-2*e  /
$$- W\left(- \frac{2}{e^{3}}\right)$$
-LambertW(-2*exp(-3))
Rapid solution [src]
       /    -3\
x1 = -W\-2*e  /
$$x_{1} = - W\left(- \frac{2}{e^{3}}\right)$$
x1 = -LambertW(-2*exp(-3))
Numerical answer [src]
x1 = 3.72763700818672
x1 = 3.72763700818672