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2*5^x+5^(x+1)+5^(x+3)=2^(x/4+1)+2^(x/4+6) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
                          x        x    
                          - + 1    - + 6
   x    x + 1    x + 3    4        4    
2*5  + 5      + 5      = 2      + 2     
$$5^{x + 3} + \left(2 \cdot 5^{x} + 5^{x + 1}\right) = 2^{\frac{x}{4} + 1} + 2^{\frac{x}{4} + 6}$$
Gráfica
Respuesta rápida [src]
        /     4     \
        | ----------|
        | log(2/625)|
x1 = log\2          /
$$x_{1} = \log{\left(2^{\frac{4}{\log{\left(\frac{2}{625} \right)}}} \right)}$$
x1 = log(2^(4/log(2/625)))
Suma y producto de raíces [src]
suma
   /     4     \
   | ----------|
   | log(2/625)|
log\2          /
$$\log{\left(2^{\frac{4}{\log{\left(\frac{2}{625} \right)}}} \right)}$$
=
   /     4     \
   | ----------|
   | log(2/625)|
log\2          /
$$\log{\left(2^{\frac{4}{\log{\left(\frac{2}{625} \right)}}} \right)}$$
producto
   /     4     \
   | ----------|
   | log(2/625)|
log\2          /
$$\log{\left(2^{\frac{4}{\log{\left(\frac{2}{625} \right)}}} \right)}$$
=
   /     4     \
   | ----------|
   | log(2/625)|
log\2          /
$$\log{\left(2^{\frac{4}{\log{\left(\frac{2}{625} \right)}}} \right)}$$
log(2^(4/log(2/625)))
Respuesta numérica [src]
x1 = -203.158819422523
x2 = -0.48264223187454
x3 = -219.158819422523
x4 = -197.158819422523
x5 = -209.158819422523
x6 = -211.158819422523
x7 = -207.158819422523
x8 = -221.158819422523
x9 = -217.158819422523
x10 = -201.158819422523
x11 = -191.158819422523
x12 = -205.158819422523
x13 = -187.158819422523
x14 = -185.158819422523
x15 = -183.158819422523
x16 = -193.158819422523
x17 = -189.158819422523
x18 = -199.158819422523
x19 = -195.158819422523
x20 = -213.158819422523
x21 = -215.158819422523
x21 = -215.158819422523