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log2^2x-log2x-2=0 equation

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Numerical solution:

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The solution

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   2                        
log (2)*x - log(2*x) - 2 = 0
(xlog⁡(2)2−log⁡(2x))−2=0\left(x \log{\left(2 \right)}^{2} - \log{\left(2 x \right)}\right) - 2 = 0
Simplify
The graph
05-10-510152025305-5
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
   /    2     -2 \    /    2     -2     \
   |-log (2)*e   |    |-log (2)*e       |
  W|-------------|   W|-------------, -1|
   \      2      /    \      2          /
- ---------------- - --------------------
         2                    2          
      log (2)              log (2)
−W(−log⁡(2)22e2)log⁡(2)2−W−1(−log⁡(2)22e2)log⁡(2)2- \frac{W\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}} - \frac{W_{-1}\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}} 
=
   /    2     -2 \    /    2     -2     \
   |-log (2)*e   |    |-log (2)*e       |
  W|-------------|   W|-------------, -1|
   \      2      /    \      2          /
- ---------------- - --------------------
         2                    2          
      log (2)              log (2)
−W(−log⁡(2)22e2)log⁡(2)2−W−1(−log⁡(2)22e2)log⁡(2)2- \frac{W\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}} - \frac{W_{-1}\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}} 
product
  /    2     -2 \    /    2     -2     \ 
  |-log (2)*e   |    |-log (2)*e       | 
-W|-------------|  -W|-------------, -1| 
  \      2      /    \      2          / 
------------------*----------------------
        2                    2           
     log (2)              log (2)
−W(−log⁡(2)22e2)log⁡(2)2(−W−1(−log⁡(2)22e2)log⁡(2)2)- \frac{W\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}} \left(- \frac{W_{-1}\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}}\right) 
=
 /    2     -2 \  /    2     -2     \
 |-log (2)*e   |  |-log (2)*e       |
W|-------------|*W|-------------, -1|
 \      2      /  \      2          /
-------------------------------------
                  4                  
               log (2)
W(−log⁡(2)22e2)W−1(−log⁡(2)22e2)log⁡(2)4\frac{W\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right) W_{-1}\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{4}} 
LambertW(-log(2)^2*exp(-2)/2)*LambertW(-log(2)^2*exp(-2)/2, -1)/log(2)^4
Rapid solution [src] 
       /    2     -2 \ 
       |-log (2)*e   | 
     -W|-------------| 
       \      2      / 
x1 = ------------------
             2         
          log (2)
x1=−W(−log⁡(2)22e2)log⁡(2)2x_{1} = - \frac{W\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}} 
       /    2     -2     \ 
       |-log (2)*e       | 
     -W|-------------, -1| 
       \      2          / 
x2 = ----------------------
               2           
            log (2)
x2=−W−1(−log⁡(2)22e2)log⁡(2)2x_{2} = - \frac{W_{-1}\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}} 
x2 = -LambertW(-exp(-2)*log(2^2/2, -1)/log(2)^2)
Numerical answer [src] 
x1 = 0.0699814999717764
x2 = 10.4993920014961
x2 = 10.4993920014961
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