exp(-15*10^(-4)*x)=0.171 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación:
e − 0.0015 x = 171 1000 e^{- 0.0015 x} = \frac{171}{1000} e − 0.0015 x = 1000 171 o
− 171 1000 + e − 0.0015 x = 0 - \frac{171}{1000} + e^{- 0.0015 x} = 0 − 1000 171 + e − 0.0015 x = 0 o
0.99850112443771 1 x = 171 1000 0.998501124437711^{x} = \frac{171}{1000} 0.99850112443771 1 x = 1000 171 o
0.99850112443771 1 x = 171 1000 0.998501124437711^{x} = \frac{171}{1000} 0.99850112443771 1 x = 1000 171 - es la ecuación exponencial más simple
Sustituimos
v = 0.99850112443771 1 x v = 0.998501124437711^{x} v = 0.99850112443771 1 x obtendremos
v − 171 1000 = 0 v - \frac{171}{1000} = 0 v − 1000 171 = 0 o
v − 171 1000 = 0 v - \frac{171}{1000} = 0 v − 1000 171 = 0 Transportamos los términos libres (sin v)
del miembro izquierdo al derecho, obtenemos:
v = 171 1000 v = \frac{171}{1000} v = 1000 171 Obtenemos la respuesta: v = 171/1000
hacemos cambio inverso
0.99850112443771 1 x = v 0.998501124437711^{x} = v 0.99850112443771 1 x = v o
x = − 666.666666666672 log ( v ) x = - 666.666666666672 \log{\left(v \right)} x = − 666.666666666672 log ( v ) Entonces la respuesta definitiva es
x 1 = log ( 171 1000 ) log ( 0.998501124437711 ) = 1177.39448165299 x_{1} = \frac{\log{\left(\frac{171}{1000} \right)}}{\log{\left(0.998501124437711 \right)}} = 1177.39448165299 x 1 = log ( 0.998501124437711 ) log ( 1000 171 ) = 1177.39448165299
Gráfica
1200 1250 1300 1350 1400 1450 1500 1550 1600 1650 1700 1750 0.165 0.175
Suma y producto de raíces
[src]
1177.39448165298 + 1177.39448165298 - 4188.79020478639*I + 1177.39448165298 + 4188.79020478639*I
( 1177.39448165298 + ( 1177.39448165298 − 4188.79020478639 i ) ) + ( 1177.39448165298 + 4188.79020478639 i ) \left(1177.39448165298 + \left(1177.39448165298 - 4188.79020478639 i\right)\right) + \left(1177.39448165298 + 4188.79020478639 i\right) ( 1177.39448165298 + ( 1177.39448165298 − 4188.79020478639 i ) ) + ( 1177.39448165298 + 4188.79020478639 i )
3532.18344495895 3532.18344495895 3532.18344495895
1177.39448165298*(1177.39448165298 - 4188.79020478639*I)*(1177.39448165298 + 4188.79020478639*I)
1177.39448165298 ( 1177.39448165298 − 4188.79020478639 i ) ( 1177.39448165298 + 4188.79020478639 i ) 1177.39448165298 \left(1177.39448165298 - 4188.79020478639 i\right) \left(1177.39448165298 + 4188.79020478639 i\right) 1177.39448165298 ( 1177.39448165298 − 4188.79020478639 i ) ( 1177.39448165298 + 4188.79020478639 i )
22290692701.7233 - 9.5367431640625e-7*I
22290692701.7233 − 9.5367431640625 ⋅ 1 0 − 7 i 22290692701.7233 - 9.5367431640625 \cdot 10^{-7} i 22290692701.7233 − 9.5367431640625 ⋅ 1 0 − 7 i
22290692701.7233 - 9.5367431640625e-7*i
x 1 = 1177.39448165298 x_{1} = 1177.39448165298 x 1 = 1177.39448165298
x2 = 1177.39448165298 - 4188.79020478639*I
x 2 = 1177.39448165298 − 4188.79020478639 i x_{2} = 1177.39448165298 - 4188.79020478639 i x 2 = 1177.39448165298 − 4188.79020478639 i
x3 = 1177.39448165298 + 4188.79020478639*I
x 3 = 1177.39448165298 + 4188.79020478639 i x_{3} = 1177.39448165298 + 4188.79020478639 i x 3 = 1177.39448165298 + 4188.79020478639 i
x3 = 1177.39448165298 + 4188.79020478639*i
x2 = 1177.39448165298 - 4188.79020478639*i
x3 = 1177.39448165298 + 4188.79020478639*i
x3 = 1177.39448165298 + 4188.79020478639*i