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log2/2(x)−5⋅log2(x)+4=0. la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
log(2)       log(x)        
------*x - 5*------ + 4 = 0
  2          log(2)
(xlog⁡(2)2−5log⁡(x)log⁡(2))+4=0\left(x \frac{\log{\left(2 \right)}}{2} - 5 \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\right) + 4 = 0
Simplificar
Gráfica
0-10102030405060708090100110120130-100100
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
          /  4/5    2        \
          |-2   *log (2)     |
     -10*W|--------------, -1|
          \      10          /
x1 = -------------------------
                 2            
              log (2)
x1=−10W−1(−245log⁡(2)210)log⁡(2)2x_{1} = - \frac{10 W_{-1}\left(- \frac{2^{\frac{4}{5}} \log{\left(2 \right)}^{2}}{10}\right)}{\log{\left(2 \right)}^{2}} 
      41   21  256   34
      --  ---  ---  ---
      46  598  299  299
     2  *3   *5   *7   
x2 = ------------------
             5
x2=24146⋅321598⋅5256299⋅7342995x_{2} = \frac{2^{\frac{41}{46}} \cdot 3^{\frac{21}{598}} \cdot 5^{\frac{256}{299}} \cdot 7^{\frac{34}{299}}}{5} 
x2 = 2^(41/46)*3^(21/598)*5^(256/299)*7^(34/299)/5
Suma y producto de raíces [src] 
suma
      /  4/5    2        \    41   21  256   34
      |-2   *log (2)     |    --  ---  ---  ---
  10*W|--------------, -1|    46  598  299  299
      \      10          /   2  *3   *5   *7   
- ------------------------ + ------------------
             2                       5         
          log (2)
24146⋅321598⋅5256299⋅7342995−10W−1(−245log⁡(2)210)log⁡(2)2\frac{2^{\frac{41}{46}} \cdot 3^{\frac{21}{598}} \cdot 5^{\frac{256}{299}} \cdot 7^{\frac{34}{299}}}{5} - \frac{10 W_{-1}\left(- \frac{2^{\frac{4}{5}} \log{\left(2 \right)}^{2}}{10}\right)}{\log{\left(2 \right)}^{2}} 
=
      /  4/5    2        \    41   21  256   34
      |-2   *log (2)     |    --  ---  ---  ---
  10*W|--------------, -1|    46  598  299  299
      \      10          /   2  *3   *5   *7   
- ------------------------ + ------------------
             2                       5         
          log (2)
24146⋅321598⋅5256299⋅7342995−10W−1(−245log⁡(2)210)log⁡(2)2\frac{2^{\frac{41}{46}} \cdot 3^{\frac{21}{598}} \cdot 5^{\frac{256}{299}} \cdot 7^{\frac{34}{299}}}{5} - \frac{10 W_{-1}\left(- \frac{2^{\frac{4}{5}} \log{\left(2 \right)}^{2}}{10}\right)}{\log{\left(2 \right)}^{2}} 
producto
     /  4/5    2        \  41   21  256   34
     |-2   *log (2)     |  --  ---  ---  ---
-10*W|--------------, -1|  46  598  299  299
     \      10          / 2  *3   *5   *7   
-------------------------*------------------
            2                     5         
         log (2)
−10W−1(−245log⁡(2)210)log⁡(2)224146⋅321598⋅5256299⋅7342995- \frac{10 W_{-1}\left(- \frac{2^{\frac{4}{5}} \log{\left(2 \right)}^{2}}{10}\right)}{\log{\left(2 \right)}^{2}} \frac{2^{\frac{41}{46}} \cdot 3^{\frac{21}{598}} \cdot 5^{\frac{256}{299}} \cdot 7^{\frac{34}{299}}}{5} 
=
    41   21  256   34                      
    --  ---  ---  ---  /  4/5    2        \
    46  598  299  299  |-2   *log (2)     |
-2*2  *3   *5   *7   *W|--------------, -1|
                       \      10          /
-------------------------------------------
                     2                     
                  log (2)
−2⋅24146⋅321598⋅5256299⋅734299W−1(−245log⁡(2)210)log⁡(2)2- \frac{2 \cdot 2^{\frac{41}{46}} \cdot 3^{\frac{21}{598}} \cdot 5^{\frac{256}{299}} \cdot 7^{\frac{34}{299}} W_{-1}\left(- \frac{2^{\frac{4}{5}} \log{\left(2 \right)}^{2}}{10}\right)}{\log{\left(2 \right)}^{2}} 
-2*2^(41/46)*3^(21/598)*5^(256/299)*7^(34/299)*LambertW(-2^(4/5)*log(2)^2/10, -1)/log(2)^2
Respuesta numérica [src] 
x1 = 79.5461742606317
x2 = 1.90827857013858
x2 = 1.90827857013858
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