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exp(1/x)=y la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
 1    
 -    
 x    
e  = y
$$e^{\frac{1}{x}} = y$$
Gráfica
Respuesta rápida [src]
           log(|y|)              I*arg(y)     
x1 = ------------------- - -------------------
        2         2           2         2     
     arg (y) + log (|y|)   arg (y) + log (|y|)
$$x_{1} = \frac{\log{\left(\left|{y}\right| \right)}}{\log{\left(\left|{y}\right| \right)}^{2} + \arg^{2}{\left(y \right)}} - \frac{i \arg{\left(y \right)}}{\log{\left(\left|{y}\right| \right)}^{2} + \arg^{2}{\left(y \right)}}$$
x1 = log(|y|)/(log(|y|)^2 + arg(y)^2) - i*arg(y)/(log(|y|)^2 + arg(y)^2)
Suma y producto de raíces [src]
suma
      log(|y|)              I*arg(y)     
------------------- - -------------------
   2         2           2         2     
arg (y) + log (|y|)   arg (y) + log (|y|)
$$\frac{\log{\left(\left|{y}\right| \right)}}{\log{\left(\left|{y}\right| \right)}^{2} + \arg^{2}{\left(y \right)}} - \frac{i \arg{\left(y \right)}}{\log{\left(\left|{y}\right| \right)}^{2} + \arg^{2}{\left(y \right)}}$$
=
      log(|y|)              I*arg(y)     
------------------- - -------------------
   2         2           2         2     
arg (y) + log (|y|)   arg (y) + log (|y|)
$$\frac{\log{\left(\left|{y}\right| \right)}}{\log{\left(\left|{y}\right| \right)}^{2} + \arg^{2}{\left(y \right)}} - \frac{i \arg{\left(y \right)}}{\log{\left(\left|{y}\right| \right)}^{2} + \arg^{2}{\left(y \right)}}$$
producto
      log(|y|)              I*arg(y)     
------------------- - -------------------
   2         2           2         2     
arg (y) + log (|y|)   arg (y) + log (|y|)
$$\frac{\log{\left(\left|{y}\right| \right)}}{\log{\left(\left|{y}\right| \right)}^{2} + \arg^{2}{\left(y \right)}} - \frac{i \arg{\left(y \right)}}{\log{\left(\left|{y}\right| \right)}^{2} + \arg^{2}{\left(y \right)}}$$
=
-I*arg(y) + log(|y|)
--------------------
   2         2      
arg (y) + log (|y|) 
$$\frac{\log{\left(\left|{y}\right| \right)} - i \arg{\left(y \right)}}{\log{\left(\left|{y}\right| \right)}^{2} + \arg^{2}{\left(y \right)}}$$
(-i*arg(y) + log(|y|))/(arg(y)^2 + log(|y|)^2)