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log(3)^(2)*x-3*log(3*x)+2=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   2                          
log (3)*x - 3*log(3*x) + 2 = 0
(xlog⁡(3)2−3log⁡(3x))+2=0\left(x \log{\left(3 \right)}^{2} - 3 \log{\left(3 x \right)}\right) + 2 = 0
Simplificar
Gráfica
05-10-5101520-2525
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
     /    2     2/3 \      /    2     2/3     \
     |-log (3)*e    |      |-log (3)*e        |
  3*W|--------------|   3*W|--------------, -1|
     \      9       /      \      9           /
- ------------------- - -----------------------
           2                       2           
        log (3)                 log (3)
−3W(−e23log⁡(3)29)log⁡(3)2−3W−1(−e23log⁡(3)29)log⁡(3)2- \frac{3 W\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}} - \frac{3 W_{-1}\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}} 
=
     /    2     2/3 \      /    2     2/3     \
     |-log (3)*e    |      |-log (3)*e        |
  3*W|--------------|   3*W|--------------, -1|
     \      9       /      \      9           /
- ------------------- - -----------------------
           2                       2           
        log (3)                 log (3)
−3W(−e23log⁡(3)29)log⁡(3)2−3W−1(−e23log⁡(3)29)log⁡(3)2- \frac{3 W\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}} - \frac{3 W_{-1}\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}} 
producto
    /    2     2/3 \     /    2     2/3     \
    |-log (3)*e    |     |-log (3)*e        |
-3*W|--------------| -3*W|--------------, -1|
    \      9       /     \      9           /
--------------------*------------------------
         2                      2            
      log (3)                log (3)
−3W(−e23log⁡(3)29)log⁡(3)2(−3W−1(−e23log⁡(3)29)log⁡(3)2)- \frac{3 W\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}} \left(- \frac{3 W_{-1}\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}}\right) 
=
   /    2     2/3 \  /    2     2/3     \
   |-log (3)*e    |  |-log (3)*e        |
9*W|--------------|*W|--------------, -1|
   \      9       /  \      9           /
-----------------------------------------
                    4                    
                 log (3)
9W(−e23log⁡(3)29)W−1(−e23log⁡(3)29)log⁡(3)4\frac{9 W\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right) W_{-1}\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{4}} 
9*LambertW(-log(3)^2*exp(2/3)/9)*LambertW(-log(3)^2*exp(2/3)/9, -1)/log(3)^4
Respuesta rápida [src] 
         /    2     2/3 \
         |-log (3)*e    |
     -3*W|--------------|
         \      9       /
x1 = --------------------
              2          
           log (3)
x1=−3W(−e23log⁡(3)29)log⁡(3)2x_{1} = - \frac{3 W\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}} 
         /    2     2/3     \
         |-log (3)*e        |
     -3*W|--------------, -1|
         \      9           /
x2 = ------------------------
                2            
             log (3)
x2=−3W−1(−e23log⁡(3)29)log⁡(3)2x_{2} = - \frac{3 W_{-1}\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}} 
x2 = -3*LambertW(-exp(2/3)*log(3^2/9, -1)/log(3)^2)
Respuesta numérica [src] 
x1 = 0.952385495396966
x2 = 5.14525737680421
x2 = 5.14525737680421
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