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6*(-2x)-5*6^(-x)-6=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
            -x        
6*-2*x - 5*6   - 6 = 0
(6(2x)56x)6=0\left(6 \left(- 2 x\right) - 5 \cdot 6^{- x}\right) - 6 = 0
Gráfica
-0.75-0.50-0.250.000.250.500.751.001.251.50-2020
Suma y producto de raíces [src]
suma
        / /     ___       \\       / /     ___       \\
        | |-5*\/ 6 *log(6)||       | |-5*\/ 6 *log(6)||
      re|W|---------------||   I*im|W|---------------||
  1     \ \       12      //       \ \       12      //
- - + ---------------------- + ------------------------
  2           log(6)                    log(6)         
12+re(W(56log(6)12))log(6)+iim(W(56log(6)12))log(6)- \frac{1}{2} + \frac{\operatorname{re}{\left(W\left(- \frac{5 \sqrt{6} \log{\left(6 \right)}}{12}\right)\right)}}{\log{\left(6 \right)}} + \frac{i \operatorname{im}{\left(W\left(- \frac{5 \sqrt{6} \log{\left(6 \right)}}{12}\right)\right)}}{\log{\left(6 \right)}}
=
        / /     ___       \\       / /     ___       \\
        | |-5*\/ 6 *log(6)||       | |-5*\/ 6 *log(6)||
      re|W|---------------||   I*im|W|---------------||
  1     \ \       12      //       \ \       12      //
- - + ---------------------- + ------------------------
  2           log(6)                    log(6)         
12+re(W(56log(6)12))log(6)+iim(W(56log(6)12))log(6)- \frac{1}{2} + \frac{\operatorname{re}{\left(W\left(- \frac{5 \sqrt{6} \log{\left(6 \right)}}{12}\right)\right)}}{\log{\left(6 \right)}} + \frac{i \operatorname{im}{\left(W\left(- \frac{5 \sqrt{6} \log{\left(6 \right)}}{12}\right)\right)}}{\log{\left(6 \right)}}
producto
        / /     ___       \\       / /     ___       \\
        | |-5*\/ 6 *log(6)||       | |-5*\/ 6 *log(6)||
      re|W|---------------||   I*im|W|---------------||
  1     \ \       12      //       \ \       12      //
- - + ---------------------- + ------------------------
  2           log(6)                    log(6)         
12+re(W(56log(6)12))log(6)+iim(W(56log(6)12))log(6)- \frac{1}{2} + \frac{\operatorname{re}{\left(W\left(- \frac{5 \sqrt{6} \log{\left(6 \right)}}{12}\right)\right)}}{\log{\left(6 \right)}} + \frac{i \operatorname{im}{\left(W\left(- \frac{5 \sqrt{6} \log{\left(6 \right)}}{12}\right)\right)}}{\log{\left(6 \right)}}
=
               / /     ___       \\     / /     ___       \\
  log(6)       | |-5*\/ 6 *log(6)||     | |-5*\/ 6 *log(6)||
- ------ + I*im|W|---------------|| + re|W|---------------||
    2          \ \       12      //     \ \       12      //
------------------------------------------------------------
                           log(6)                           
log(6)2+re(W(56log(6)12))+iim(W(56log(6)12))log(6)\frac{- \frac{\log{\left(6 \right)}}{2} + \operatorname{re}{\left(W\left(- \frac{5 \sqrt{6} \log{\left(6 \right)}}{12}\right)\right)} + i \operatorname{im}{\left(W\left(- \frac{5 \sqrt{6} \log{\left(6 \right)}}{12}\right)\right)}}{\log{\left(6 \right)}}
(-log(6)/2 + i*im(LambertW(-5*sqrt(6)*log(6)/12)) + re(LambertW(-5*sqrt(6)*log(6)/12)))/log(6)
Respuesta rápida [src]
             / /     ___       \\       / /     ___       \\
             | |-5*\/ 6 *log(6)||       | |-5*\/ 6 *log(6)||
           re|W|---------------||   I*im|W|---------------||
       1     \ \       12      //       \ \       12      //
x1 = - - + ---------------------- + ------------------------
       2           log(6)                    log(6)         
x1=12+re(W(56log(6)12))log(6)+iim(W(56log(6)12))log(6)x_{1} = - \frac{1}{2} + \frac{\operatorname{re}{\left(W\left(- \frac{5 \sqrt{6} \log{\left(6 \right)}}{12}\right)\right)}}{\log{\left(6 \right)}} + \frac{i \operatorname{im}{\left(W\left(- \frac{5 \sqrt{6} \log{\left(6 \right)}}{12}\right)\right)}}{\log{\left(6 \right)}}
x1 = -1/2 + re(LambertW(-5*sqrt(6)*log(6)/12))/log(6) + i*im(LambertW(-5*sqrt(6)*log(6)/12))/log(6)
Respuesta numérica [src]
x1 = -0.439419334754449 + 0.913630996612125*i
x1 = -0.439419334754449 + 0.913630996612125*i