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log3^2x=4-3log3x la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   2                      
log (3)*x = 4 - 3*log(3*x)
$$x \log{\left(3 \right)}^{2} = 4 - 3 \log{\left(3 x \right)}$$
Gráfica
Respuesta rápida [src]
        /   2     4/3\
        |log (3)*e   |
     3*W|------------|
        \     9      /
x1 = -----------------
             2        
          log (3)     
$$x_{1} = \frac{3 W\left(\frac{e^{\frac{4}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}}$$
x1 = 3*LambertW(exp(4/3)*log(3)^2/9)/log(3)^2
Suma y producto de raíces [src]
suma
   /   2     4/3\
   |log (3)*e   |
3*W|------------|
   \     9      /
-----------------
        2        
     log (3)     
$$\frac{3 W\left(\frac{e^{\frac{4}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}}$$
=
   /   2     4/3\
   |log (3)*e   |
3*W|------------|
   \     9      /
-----------------
        2        
     log (3)     
$$\frac{3 W\left(\frac{e^{\frac{4}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}}$$
producto
   /   2     4/3\
   |log (3)*e   |
3*W|------------|
   \     9      /
-----------------
        2        
     log (3)     
$$\frac{3 W\left(\frac{e^{\frac{4}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}}$$
=
   /   2     4/3\
   |log (3)*e   |
3*W|------------|
   \     9      /
-----------------
        2        
     log (3)     
$$\frac{3 W\left(\frac{e^{\frac{4}{3}} \log{\left(3 \right)}^{2}}{9}\right)}{\log{\left(3 \right)}^{2}}$$
3*LambertW(log(3)^2*exp(4/3)/9)/log(3)^2
Respuesta numérica [src]
x1 = 0.885547509289821
x1 = 0.885547509289821