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(1/512)^(x+4)=8^-x la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   -4 - x    -x
512       = 8
$$\left(\frac{1}{512}\right)^{x + 4} = 8^{- x}$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = -6
$$x_{1} = -6$$ 
       log(64)    pi*I 
x2 = - ------- + ------
        log(2)   log(2)
$$x_{2} = - \frac{\log{\left(64 \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}$$ 
       log(262144)     pi*I  
x3 = - ----------- + --------
         3*log(2)    3*log(2)
$$x_{3} = - \frac{\log{\left(262144 \right)}}{3 \log{\left(2 \right)}} + \frac{i \pi}{3 \log{\left(2 \right)}}$$ 
       log(262144)    2*pi*I 
x4 = - ----------- + --------
         3*log(2)    3*log(2)
$$x_{4} = - \frac{\log{\left(262144 \right)}}{3 \log{\left(2 \right)}} + \frac{2 i \pi}{3 \log{\left(2 \right)}}$$ 
       log(262144)     pi*I  
x5 = - ----------- - --------
         3*log(2)    3*log(2)
$$x_{5} = - \frac{\log{\left(262144 \right)}}{3 \log{\left(2 \right)}} - \frac{i \pi}{3 \log{\left(2 \right)}}$$ 
       log(262144)    2*pi*I 
x6 = - ----------- - --------
         3*log(2)    3*log(2)
$$x_{6} = - \frac{\log{\left(262144 \right)}}{3 \log{\left(2 \right)}} - \frac{2 i \pi}{3 \log{\left(2 \right)}}$$ 
x6 = -log(262144)/(3*log(2)) - 2*i*pi/(3*log(2))
Suma y producto de raíces [src] 
suma
       log(64)    pi*I      log(262144)     pi*I       log(262144)    2*pi*I      log(262144)     pi*I       log(262144)    2*pi*I 
-6 + - ------- + ------ + - ----------- + -------- + - ----------- + -------- + - ----------- - -------- + - ----------- - --------
        log(2)   log(2)       3*log(2)    3*log(2)       3*log(2)    3*log(2)       3*log(2)    3*log(2)       3*log(2)    3*log(2)
$$\left(- \frac{\log{\left(262144 \right)}}{3 \log{\left(2 \right)}} - \frac{2 i \pi}{3 \log{\left(2 \right)}}\right) + \left(\left(- \frac{\log{\left(262144 \right)}}{3 \log{\left(2 \right)}} - \frac{i \pi}{3 \log{\left(2 \right)}}\right) + \left(\left(- \frac{\log{\left(262144 \right)}}{3 \log{\left(2 \right)}} + \frac{2 i \pi}{3 \log{\left(2 \right)}}\right) + \left(\left(- \frac{\log{\left(262144 \right)}}{3 \log{\left(2 \right)}} + \frac{i \pi}{3 \log{\left(2 \right)}}\right) + \left(-6 + \left(- \frac{\log{\left(64 \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}\right)\right)\right)\right)\right)$$ 
=
     log(64)   4*log(262144)    pi*I 
-6 - ------- - ------------- + ------
      log(2)      3*log(2)     log(2)
$$- \frac{4 \log{\left(262144 \right)}}{3 \log{\left(2 \right)}} - 6 - \frac{\log{\left(64 \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}$$ 
producto
   /  log(64)    pi*I \ /  log(262144)     pi*I  \ /  log(262144)    2*pi*I \ /  log(262144)     pi*I  \ /  log(262144)    2*pi*I \
-6*|- ------- + ------|*|- ----------- + --------|*|- ----------- + --------|*|- ----------- - --------|*|- ----------- - --------|
   \   log(2)   log(2)/ \    3*log(2)    3*log(2)/ \    3*log(2)    3*log(2)/ \    3*log(2)    3*log(2)/ \    3*log(2)    3*log(2)/
$$- 6 \left(- \frac{\log{\left(64 \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}\right) \left(- \frac{\log{\left(262144 \right)}}{3 \log{\left(2 \right)}} + \frac{i \pi}{3 \log{\left(2 \right)}}\right) \left(- \frac{\log{\left(262144 \right)}}{3 \log{\left(2 \right)}} + \frac{2 i \pi}{3 \log{\left(2 \right)}}\right) \left(- \frac{\log{\left(262144 \right)}}{3 \log{\left(2 \right)}} - \frac{i \pi}{3 \log{\left(2 \right)}}\right) \left(- \frac{\log{\left(262144 \right)}}{3 \log{\left(2 \right)}} - \frac{2 i \pi}{3 \log{\left(2 \right)}}\right)$$ 
=
2*(pi*I + log(262144))*(-pi*I + log(64))*(-pi*I + log(262144))*(-2*pi*I + log(262144))*(2*pi*I + log(262144))
-------------------------------------------------------------------------------------------------------------
                                                        5                                                    
                                                  27*log (2)
$$\frac{2 \left(\log{\left(64 \right)} - i \pi\right) \left(\log{\left(262144 \right)} - 2 i \pi\right) \left(\log{\left(262144 \right)} - i \pi\right) \left(\log{\left(262144 \right)} + i \pi\right) \left(\log{\left(262144 \right)} + 2 i \pi\right)}{27 \log{\left(2 \right)}^{5}}$$ 
2*(pi*i + log(262144))*(-pi*i + log(64))*(-pi*i + log(262144))*(-2*pi*i + log(262144))*(2*pi*i + log(262144))/(27*log(2)^5)
Respuesta numérica [src] 
x1 = 58.2742094753799
x2 = 32.2742094753799
x3 = 22.2742094753799
x4 = -6.0
x5 = 24.2742094753799
x6 = 16.2742094753799
x7 = 30.2742094753799
x8 = 40.2742094753799
x9 = 96.2742094753799
x10 = 64.2742094753799
x11 = 44.2742094753799
x12 = 62.2742094753799
x13 = 34.2742094753799
x14 = 84.2742094753799
x15 = 108.27420947538
x16 = 18.2742094753799
x17 = 50.2742094753799
x18 = 20.2742094753799
x19 = 110.27420947538
x20 = 82.2742094753799
x21 = 80.2742094753799
x22 = 26.2742094753799
x23 = 68.2742094753799
x24 = 60.2742094753799
x25 = 52.2742094753799
x26 = 76.2742094753799
x27 = 90.2742094753799
x28 = 38.2742094753799
x29 = 48.2742094753799
x30 = 106.27420947538
x31 = 92.2742094753799
x32 = 54.2742094753799
x33 = 70.2742094753799
x34 = 86.2742094753799
x35 = 14.2742094753799
x36 = 74.2742094753799
x37 = 36.2742094753799
x38 = 46.2742094753799
x39 = 56.2742094753799
x40 = 104.27420947538
x41 = 78.2742094753799
x42 = 100.27420947538
x43 = 42.2742094753799
x44 = 66.2742094753799
x45 = 72.2742094753799
x46 = 102.27420947538
x47 = 28.2742094753799
x48 = 88.2742094753799
x49 = 94.2742094753799
x50 = 98.2742094753799
x50 = 98.2742094753799
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