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log(5)*x^2*log(x)*5+3=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
        2                 
log(5)*x *log(x)*5 + 3 = 0
5x2log⁡(5)log⁡(x)+3=05 x^{2} \log{\left(5 \right)} \log{\left(x \right)} + 3 = 0
Simplificar
Gráfica
-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.5020
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
                        / /  -6    \\        / /  -6    \\                     
                      re|W|--------||      re|W|--------||                     
   /  / /  -6    \\\    \ \5*log(5)//        \ \5*log(5)//    /  / /  -6    \\\
   |im|W|--------|||  ---------------      ---------------    |im|W|--------|||
   |  \ \5*log(5)//|         2                    2           |  \ \5*log(5)//|
cos|---------------|*e                + I*e               *sin|---------------|
   \       2       /                                          \       2       /
cos⁡(im⁡(W(−65log⁡(5)))2)e−re⁡(W(−65log⁡(5)))2+isin⁡(im⁡(W(−65log⁡(5)))2)e−re⁡(W(−65log⁡(5)))2\frac{\cos{\left(\frac{\operatorname{im}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2} \right)}}{e^{- \frac{\operatorname{re}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2}}} + \frac{i \sin{\left(\frac{\operatorname{im}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2} \right)}}{e^{- \frac{\operatorname{re}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2}}} 
=
                        / /  -6    \\        / /  -6    \\                     
                      re|W|--------||      re|W|--------||                     
   /  / /  -6    \\\    \ \5*log(5)//        \ \5*log(5)//    /  / /  -6    \\\
   |im|W|--------|||  ---------------      ---------------    |im|W|--------|||
   |  \ \5*log(5)//|         2                    2           |  \ \5*log(5)//|
cos|---------------|*e                + I*e               *sin|---------------|
   \       2       /                                          \       2       /
cos⁡(im⁡(W(−65log⁡(5)))2)e−re⁡(W(−65log⁡(5)))2+isin⁡(im⁡(W(−65log⁡(5)))2)e−re⁡(W(−65log⁡(5)))2\frac{\cos{\left(\frac{\operatorname{im}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2} \right)}}{e^{- \frac{\operatorname{re}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2}}} + \frac{i \sin{\left(\frac{\operatorname{im}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2} \right)}}{e^{- \frac{\operatorname{re}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2}}} 
producto
                        / /  -6    \\        / /  -6    \\                     
                      re|W|--------||      re|W|--------||                     
   /  / /  -6    \\\    \ \5*log(5)//        \ \5*log(5)//    /  / /  -6    \\\
   |im|W|--------|||  ---------------      ---------------    |im|W|--------|||
   |  \ \5*log(5)//|         2                    2           |  \ \5*log(5)//|
cos|---------------|*e                + I*e               *sin|---------------|
   \       2       /                                          \       2       /
cos⁡(im⁡(W(−65log⁡(5)))2)e−re⁡(W(−65log⁡(5)))2+isin⁡(im⁡(W(−65log⁡(5)))2)e−re⁡(W(−65log⁡(5)))2\frac{\cos{\left(\frac{\operatorname{im}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2} \right)}}{e^{- \frac{\operatorname{re}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2}}} + \frac{i \sin{\left(\frac{\operatorname{im}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2} \right)}}{e^{- \frac{\operatorname{re}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2}}} 
=
   / /  -6    \\       / /  -6    \\
 re|W|--------||   I*im|W|--------||
   \ \5*log(5)//       \ \5*log(5)//
 --------------- + -----------------
        2                  2        
e
ere⁡(W(−65log⁡(5)))2+iim⁡(W(−65log⁡(5)))2e^{\frac{\operatorname{re}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2} + \frac{i \operatorname{im}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2}} 
exp(re(LambertW(-6/(5*log(5))))/2 + i*im(LambertW(-6/(5*log(5))))/2)
Respuesta rápida [src] 
                             / /  -6    \\        / /  -6    \\                     
                           re|W|--------||      re|W|--------||                     
        /  / /  -6    \\\    \ \5*log(5)//        \ \5*log(5)//    /  / /  -6    \\\
        |im|W|--------|||  ---------------      ---------------    |im|W|--------|||
        |  \ \5*log(5)//|         2                    2           |  \ \5*log(5)//|
x1 = cos|---------------|*e                + I*e               *sin|---------------|
        \       2       /                                          \       2       /
x1=cos⁡(im⁡(W(−65log⁡(5)))2)e−re⁡(W(−65log⁡(5)))2+isin⁡(im⁡(W(−65log⁡(5)))2)e−re⁡(W(−65log⁡(5)))2x_{1} = \frac{\cos{\left(\frac{\operatorname{im}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2} \right)}}{e^{- \frac{\operatorname{re}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2}}} + \frac{i \sin{\left(\frac{\operatorname{im}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2} \right)}}{e^{- \frac{\operatorname{re}{\left(W\left(- \frac{6}{5 \log{\left(5 \right)}}\right)\right)}}{2}}} 
x1 = exp(re(LambertW(-6/(5*log(5))))/2)*cos(im(LambertW(-6/(5*log(5))))/2) + i*exp(re(LambertW(-6/(5*log(5))))/2)*sin(im(LambertW(-6/(5*log(5))))/2)
Respuesta numérica [src] 
x1 = 0.648114668479384 + 0.416622973917153*i
x2 = 0.648114668479384 - 0.416622973917153*i
x3 = 0.648114668479388 - 0.416622973917148*i
x4 = 0.648114668479384 + 0.416622973917154*i
x4 = 0.648114668479384 + 0.416622973917154*i
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