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3^x+5x-2=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
 x              
3  + 5*x - 2 = 0
$$\left(3^{x} + 5 x\right) - 2 = 0$$
Gráfica
Suma y producto de raíces [src]
suma
   /   /  2/5\\         
   |   | 3   ||         
   |   | ----||         
   |   |  5  ||   log(9)
- W\log\3    // + ------
                    5   
------------------------
         log(3)         
$$\frac{- W\left(\log{\left(3^{\frac{3^{\frac{2}{5}}}{5}} \right)}\right) + \frac{\log{\left(9 \right)}}{5}}{\log{\left(3 \right)}}$$
=
   /   /  2/5\\         
   |   | 3   ||         
   |   | ----||         
   |   |  5  ||   log(9)
- W\log\3    // + ------
                    5   
------------------------
         log(3)         
$$\frac{- W\left(\log{\left(3^{\frac{3^{\frac{2}{5}}}{5}} \right)}\right) + \frac{\log{\left(9 \right)}}{5}}{\log{\left(3 \right)}}$$
producto
   /   /  2/5\\         
   |   | 3   ||         
   |   | ----||         
   |   |  5  ||   log(9)
- W\log\3    // + ------
                    5   
------------------------
         log(3)         
$$\frac{- W\left(\log{\left(3^{\frac{3^{\frac{2}{5}}}{5}} \right)}\right) + \frac{\log{\left(9 \right)}}{5}}{\log{\left(3 \right)}}$$
=
   /   /  2/5\\         
   |   | 3   ||         
   |   | ----||         
   |   |  5  ||   log(9)
- W\log\3    // + ------
                    5   
------------------------
         log(3)         
$$\frac{- W\left(\log{\left(3^{\frac{3^{\frac{2}{5}}}{5}} \right)}\right) + \frac{\log{\left(9 \right)}}{5}}{\log{\left(3 \right)}}$$
(-LambertW(log(3^(3^(2/5)/5))) + log(9)/5)/log(3)
Respuesta rápida [src]
        /   /  2/5\\         
        |   | 3   ||         
        |   | ----||         
        |   |  5  ||   log(9)
     - W\log\3    // + ------
                         5   
x1 = ------------------------
              log(3)         
$$x_{1} = \frac{- W\left(\log{\left(3^{\frac{3^{\frac{2}{5}}}{5}} \right)}\right) + \frac{\log{\left(9 \right)}}{5}}{\log{\left(3 \right)}}$$
x1 = (-LambertW(log(3^(3^(2/5)/5))) + log(9)/5)/log(3)
Respuesta numérica [src]
x1 = 0.161240236683631
x1 = 0.161240236683631