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(0,25)^(1-2x)=64 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
 -1 + 2*x     
4         = 64
(14)1−2x=64\left(\frac{1}{4}\right)^{1 - 2 x} = 64
Simplificar
Solución detallada
Tenemos la ecuación:
(14)1−2x=64\left(\frac{1}{4}\right)^{1 - 2 x} = 64
o
(14)1−2x−64=0\left(\frac{1}{4}\right)^{1 - 2 x} - 64 = 0
o
16x4=64\frac{16^{x}}{4} = 64
o
16x=25616^{x} = 256
- es la ecuación exponencial más simple
Sustituimos
v=16xv = 16^{x}
obtendremos
v−256=0v - 256 = 0
o
v−256=0v - 256 = 0
Transportamos los términos libres (sin v)
del miembro izquierdo al derecho, obtenemos:
v=256v = 256
Obtenemos la respuesta: v = 256
hacemos cambio inverso
16x=v16^{x} = v
o
x=log⁡(v)log⁡(16)x = \frac{\log{\left(v \right)}}{\log{\left(16 \right)}}
Entonces la respuesta definitiva es
x1=log⁡(256)log⁡(16)=2x_{1} = \frac{\log{\left(256 \right)}}{\log{\left(16 \right)}} = 2
Gráfica
-10.0-7.5-5.0-2.50.02.55.07.510.012.515.017.50100000000000000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = 2
x1=2x_{1} = 2 
     log(4)    pi*I 
x2 = ------ + ------
     log(2)   log(2)
x2=log⁡(4)log⁡(2)+iπlog⁡(2)x_{2} = \frac{\log{\left(4 \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}} 
     log(16)      pi*I  
x3 = -------- - --------
     2*log(2)   2*log(2)
x3=log⁡(16)2log⁡(2)−iπ2log⁡(2)x_{3} = \frac{\log{\left(16 \right)}}{2 \log{\left(2 \right)}} - \frac{i \pi}{2 \log{\left(2 \right)}} 
     log(16)      pi*I  
x4 = -------- + --------
     2*log(2)   2*log(2)
x4=log⁡(16)2log⁡(2)+iπ2log⁡(2)x_{4} = \frac{\log{\left(16 \right)}}{2 \log{\left(2 \right)}} + \frac{i \pi}{2 \log{\left(2 \right)}} 
x4 = log(16)/(2*log(2)) + i*pi/(2*log(2))
Suma y producto de raíces [src] 
suma
    log(4)    pi*I    log(16)      pi*I     log(16)      pi*I  
2 + ------ + ------ + -------- - -------- + -------- + --------
    log(2)   log(2)   2*log(2)   2*log(2)   2*log(2)   2*log(2)
(log⁡(16)2log⁡(2)+iπ2log⁡(2))+((log⁡(16)2log⁡(2)−iπ2log⁡(2))+(2+(log⁡(4)log⁡(2)+iπlog⁡(2))))\left(\frac{\log{\left(16 \right)}}{2 \log{\left(2 \right)}} + \frac{i \pi}{2 \log{\left(2 \right)}}\right) + \left(\left(\frac{\log{\left(16 \right)}}{2 \log{\left(2 \right)}} - \frac{i \pi}{2 \log{\left(2 \right)}}\right) + \left(2 + \left(\frac{\log{\left(4 \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}\right)\right)\right) 
=
    log(4)   log(16)    pi*I 
2 + ------ + ------- + ------
    log(2)    log(2)   log(2)
2+log⁡(4)log⁡(2)+log⁡(16)log⁡(2)+iπlog⁡(2)2 + \frac{\log{\left(4 \right)}}{\log{\left(2 \right)}} + \frac{\log{\left(16 \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}} 
producto
  /log(4)    pi*I \ /log(16)      pi*I  \ /log(16)      pi*I  \
2*|------ + ------|*|-------- - --------|*|-------- + --------|
  \log(2)   log(2)/ \2*log(2)   2*log(2)/ \2*log(2)   2*log(2)/
2(log⁡(4)log⁡(2)+iπlog⁡(2))(log⁡(16)2log⁡(2)−iπ2log⁡(2))(log⁡(16)2log⁡(2)+iπ2log⁡(2))2 \left(\frac{\log{\left(4 \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}\right) \left(\frac{\log{\left(16 \right)}}{2 \log{\left(2 \right)}} - \frac{i \pi}{2 \log{\left(2 \right)}}\right) \left(\frac{\log{\left(16 \right)}}{2 \log{\left(2 \right)}} + \frac{i \pi}{2 \log{\left(2 \right)}}\right) 
=
(pi*I + log(4))*(pi*I + log(16))*(-pi*I + log(16))
--------------------------------------------------
                         3                        
                    2*log (2)
(log⁡(4)+iπ)(log⁡(16)−iπ)(log⁡(16)+iπ)2log⁡(2)3\frac{\left(\log{\left(4 \right)} + i \pi\right) \left(\log{\left(16 \right)} - i \pi\right) \left(\log{\left(16 \right)} + i \pi\right)}{2 \log{\left(2 \right)}^{3}} 
(pi*i + log(4))*(pi*i + log(16))*(-pi*i + log(16))/(2*log(2)^3)
Respuesta numérica [src] 
x1 = 2.0
x2 = 2.0 + 4.53236014182719*i
x3 = 2.0 - 2.2661800709136*i
x4 = 2.0 + 2.2661800709136*i
x4 = 2.0 + 2.2661800709136*i
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