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exp(-15*10^(-4)*x)=0.171 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
 -0.0015*x   171 
e          = ----
             1000
e0.0015x=1711000e^{- 0.0015 x} = \frac{171}{1000}
Solución detallada
Tenemos la ecuación:
e0.0015x=1711000e^{- 0.0015 x} = \frac{171}{1000}
o
1711000+e0.0015x=0- \frac{171}{1000} + e^{- 0.0015 x} = 0
o
0.998501124437711x=17110000.998501124437711^{x} = \frac{171}{1000}
o
0.998501124437711x=17110000.998501124437711^{x} = \frac{171}{1000}
- es la ecuación exponencial más simple
Sustituimos
v=0.998501124437711xv = 0.998501124437711^{x}
obtendremos
v1711000=0v - \frac{171}{1000} = 0
o
v1711000=0v - \frac{171}{1000} = 0
Transportamos los términos libres (sin v)
del miembro izquierdo al derecho, obtenemos:
v=1711000v = \frac{171}{1000}
Obtenemos la respuesta: v = 171/1000
hacemos cambio inverso
0.998501124437711x=v0.998501124437711^{x} = v
o
x=666.666666666672log(v)x = - 666.666666666672 \log{\left(v \right)}
Entonces la respuesta definitiva es
x1=log(1711000)log(0.998501124437711)=1177.39448165299x_{1} = \frac{\log{\left(\frac{171}{1000} \right)}}{\log{\left(0.998501124437711 \right)}} = 1177.39448165299
Gráfica
1200125013001350140014501500155016001650170017500.1650.175
Suma y producto de raíces [src]
suma
1177.39448165298 + 1177.39448165298 - 4188.79020478639*I + 1177.39448165298 + 4188.79020478639*I
(1177.39448165298+(1177.394481652984188.79020478639i))+(1177.39448165298+4188.79020478639i)\left(1177.39448165298 + \left(1177.39448165298 - 4188.79020478639 i\right)\right) + \left(1177.39448165298 + 4188.79020478639 i\right)
=
3532.18344495895
3532.183444958953532.18344495895
producto
1177.39448165298*(1177.39448165298 - 4188.79020478639*I)*(1177.39448165298 + 4188.79020478639*I)
1177.39448165298(1177.394481652984188.79020478639i)(1177.39448165298+4188.79020478639i)1177.39448165298 \left(1177.39448165298 - 4188.79020478639 i\right) \left(1177.39448165298 + 4188.79020478639 i\right)
=
22290692701.7233 - 9.5367431640625e-7*I
22290692701.72339.5367431640625107i22290692701.7233 - 9.5367431640625 \cdot 10^{-7} i
22290692701.7233 - 9.5367431640625e-7*i
Respuesta rápida [src]
x1 = 1177.39448165298
x1=1177.39448165298x_{1} = 1177.39448165298
x2 = 1177.39448165298 - 4188.79020478639*I
x2=1177.394481652984188.79020478639ix_{2} = 1177.39448165298 - 4188.79020478639 i
x3 = 1177.39448165298 + 4188.79020478639*I
x3=1177.39448165298+4188.79020478639ix_{3} = 1177.39448165298 + 4188.79020478639 i
x3 = 1177.39448165298 + 4188.79020478639*i
Respuesta numérica [src]
x1 = 1177.39448165298
x2 = 1177.39448165298 - 4188.79020478639*i
x3 = 1177.39448165298 + 4188.79020478639*i
x3 = 1177.39448165298 + 4188.79020478639*i