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(8/2)^(x+8)=6^x

(8/2)^(x+8)=6^x la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
 x + 8    x
4      = 6 
$$4^{x + 8} = 6^{x}$$
Gráfica
Respuesta rápida [src]
         /    16   \
         | --------|
         | log(2/3)|
x1 = -log\2        /
$$x_{1} = - \log{\left(2^{\frac{16}{\log{\left(\frac{2}{3} \right)}}} \right)}$$
x1 = -log(2^(16/log(2/3)))
Suma y producto de raíces [src]
suma
    /    16   \
    | --------|
    | log(2/3)|
-log\2        /
$$- \log{\left(2^{\frac{16}{\log{\left(\frac{2}{3} \right)}}} \right)}$$
=
    /    16   \
    | --------|
    | log(2/3)|
-log\2        /
$$- \log{\left(2^{\frac{16}{\log{\left(\frac{2}{3} \right)}}} \right)}$$
producto
    /    16   \
    | --------|
    | log(2/3)|
-log\2        /
$$- \log{\left(2^{\frac{16}{\log{\left(\frac{2}{3} \right)}}} \right)}$$
=
    /    16   \
    | --------|
    | log(2/3)|
-log\2        /
$$- \log{\left(2^{\frac{16}{\log{\left(\frac{2}{3} \right)}}} \right)}$$
-log(2^(16/log(2/3)))
Respuesta numérica [src]
x1 = -35.0161482996487
x2 = -73.0161482956131
x3 = -95.0161482956131
x4 = -49.0161482956269
x5 = -69.0161482956131
x6 = -29.0161483415815
x7 = -61.0161482956132
x8 = -55.0161482956143
x9 = -43.0161482957705
x10 = -47.0161482956442
x11 = -107.016148295613
x12 = -75.0161482956131
x13 = -33.0161483046933
x14 = -105.016148295613
x15 = -79.0161482956131
x16 = -41.0161482959674
x17 = -77.0161482956131
x18 = -93.0161482956131
x19 = -87.0161482956131
x20 = -37.0161482974067
x21 = -63.0161482956131
x22 = -67.0161482956131
x23 = -115.016148295613
x24 = -51.0161482956192
x25 = -101.016148295613
x26 = -111.016148295613
x27 = -59.0161482956133
x28 = -99.0161482956131
x29 = -109.016148295613
x30 = -85.0161482956131
x31 = -53.0161482956158
x32 = -31.0161483160435
x33 = -91.0161482956131
x34 = -113.016148295613
x35 = -97.0161482956131
x36 = -71.0161482956131
x37 = -103.016148295613
x38 = -65.0161482956131
x39 = -89.0161482956131
x40 = -81.0161482956131
x41 = -39.0161482964102
x42 = -45.0161482956831
x43 = -83.0161482956131
x44 = -57.0161482956136
x44 = -57.0161482956136
Gráfico
(8/2)^(x+8)=6^x la ecuación