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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
$$\left(x \log{\left(3 \right)}^{2} - 3 \log{\left(3 x \right)}\right) + 2 = 0$$
Gráfica
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)        
$$- \frac{3 W\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}} - \frac{3 W_{-1}\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}}$$
=
     /    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)        
$$- \frac{3 W\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}} - \frac{3 W_{-1}\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}}$$
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)         
$$- \frac{3 W\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}} \left(- \frac{3 W_{-1}\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}}\right)$$
=
   /    2     2/3 \  /    2     2/3     \
   |-log (3)*e    |  |-log (3)*e        |
9*W|--------------|*W|--------------, -1|
   \      9       /  \      9           /
-----------------------------------------
                    4                    
                 log (3)                 
$$\frac{9 W\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right) W_{-1}\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{4}}$$
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)       
$$x_{1} = - \frac{3 W\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}}$$
         /    2     2/3     \
         |-log (3)*e        |
     -3*W|--------------, -1|
         \      9           /
x2 = ------------------------
                2            
             log (3)         
$$x_{2} = - \frac{3 W_{-1}\left(- \frac{e^{\frac{2}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}}$$
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