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2^(4x-3)-7^(4x-1)-2^(4x)-7^(4x-2)=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
 4*x - 3    4*x - 1    4*x    4*x - 2    
2        - 7        - 2    - 7        = 0
$$- 7^{4 x - 2} + \left(- 2^{4 x} + \left(2^{4 x - 3} - 7^{4 x - 1}\right)\right) = 0$$
Gráfica
Respuesta rápida [src]
         / 64\            
      log|---|            
         \343/      pi*I  
x1 = --------- + ---------
        / 16 \      / 16 \
     log|----|   log|----|
        \2401/      \2401/
$$x_{1} = \frac{\log{\left(\frac{64}{343} \right)}}{\log{\left(\frac{16}{2401} \right)}} + \frac{i \pi}{\log{\left(\frac{16}{2401} \right)}}$$
x1 = log(64/343)/log(16/2401) + i*pi/log(16/2401)
Suma y producto de raíces [src]
suma
    / 64\            
 log|---|            
    \343/      pi*I  
--------- + ---------
   / 16 \      / 16 \
log|----|   log|----|
   \2401/      \2401/
$$\frac{\log{\left(\frac{64}{343} \right)}}{\log{\left(\frac{16}{2401} \right)}} + \frac{i \pi}{\log{\left(\frac{16}{2401} \right)}}$$
=
    / 64\            
 log|---|            
    \343/      pi*I  
--------- + ---------
   / 16 \      / 16 \
log|----|   log|----|
   \2401/      \2401/
$$\frac{\log{\left(\frac{64}{343} \right)}}{\log{\left(\frac{16}{2401} \right)}} + \frac{i \pi}{\log{\left(\frac{16}{2401} \right)}}$$
producto
    / 64\            
 log|---|            
    \343/      pi*I  
--------- + ---------
   / 16 \      / 16 \
log|----|   log|----|
   \2401/      \2401/
$$\frac{\log{\left(\frac{64}{343} \right)}}{\log{\left(\frac{16}{2401} \right)}} + \frac{i \pi}{\log{\left(\frac{16}{2401} \right)}}$$
=
          / 64\
pi*I + log|---|
          \343/
---------------
      / 16 \   
   log|----|   
      \2401/   
$$\frac{\log{\left(\frac{64}{343} \right)} + i \pi}{\log{\left(\frac{16}{2401} \right)}}$$
(pi*i + log(64/343))/log(16/2401)
Respuesta numérica [src]
x1 = -81.4412124948754
x2 = -25.4412124948754
x3 = -69.4412124948754
x4 = -59.4412124948754
x5 = -17.4412124948754
x6 = -23.4412124948754
x7 = -67.4412124948754
x8 = -55.4412124948754
x9 = -97.4412124948754
x10 = -83.4412124948754
x11 = -107.441212494875
x12 = -95.4412124948754
x13 = -27.4412124948754
x14 = -65.4412124948754
x15 = -71.4412124948754
x16 = -15.4412124948754
x17 = -35.4412124948754
x18 = -61.4412124948754
x19 = -43.4412124948754
x20 = -73.4412124948754
x21 = -91.4412124948754
x22 = -33.4412124948754
x23 = -85.4412124948754
x24 = -63.4412124948754
x25 = -19.4412124948754
x26 = -99.4412124948754
x27 = -47.4412124948754
x28 = -53.4412124948754
x29 = -39.4412124948754
x30 = -11.4412124942755
x31 = -49.4412124948754
x32 = -51.4412124948754
x33 = -57.4412124948754
x34 = -101.441212494875
x35 = -31.4412124948754
x36 = -21.4412124948754
x37 = -105.441212494875
x38 = -79.4412124948754
x39 = -13.4412124948754
x40 = -41.4412124948754
x41 = -29.4412124948754
x42 = -75.4412124948754
x43 = -103.441212494875
x44 = -77.4412124948754
x45 = -37.4412124948754
x46 = -89.4412124948754
x47 = -93.4412124948754
x48 = -87.4412124948754
x49 = -45.4412124948754
x49 = -45.4412124948754