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8=60x-1800+(1800)/(e^{x/(30))}

Solución

8 = 60 x - 1800 + \frac{1800}{e ^{\frac{x}{30}}}

Solución

x = 30 W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}, x = 30 W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

+1

Notación decimal

x = - 2.78467 \dots, x = 2.87357 \dots

Pasos de solución

8 = 60 x - 1800 + \frac{1800}{e ^{\frac{x}{30}}}

Preparar

8 = 60 x - 1800 + \frac{1800}{e ^{\frac{x}{30}}}

para la forma de Lambert:

1800 = (- 60 x + 1808) e^{\frac{x}{30}}

Re-escribir la ecuación con

\frac{1}{30} x - \frac{226}{225} = u

y

x = 30 u + \frac{452}{15}

1800 = (- 60 (30 u + \frac{452}{15}) + 1808) e^{\frac{( 30 u + \frac{452}{15} )}{30}}

Simplificar

1800 = - 1800 e^{\frac{225 u + 226}{225}} u

Reescribir

1800 = - 1800 e^{\frac{225 u + 226}{225}} u

en forma de Lambert:

e^{u} u = - \frac{1}{e ^{\frac{226}{225}}}

Resolver

e^{u} u = - \frac{1}{e ^{\frac{226}{225}}} : u = W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}), u = W_{0} (- \frac{1}{e ^{\frac{226}{225}}})

u = W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}), u = W_{0} (- \frac{1}{e ^{\frac{226}{225}}})

Sustituir hacia atrás la

u = \frac{1}{30} x - \frac{226}{225},

resolver para

x

Resolver

\frac{1}{30} x - \frac{226}{225} = W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) : x = 30 W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

Resolver

\frac{1}{30} x - \frac{226}{225} = W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) : x = 30 W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

x = 30 W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}, x = 30 W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

Verificar las soluciones:

x = 30 W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

Verdadero

, x = 30 W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

Verdadero

Las soluciones son

x = 30 W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}, x = 30 W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

Verificar las soluciones:

x = 30 W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

Verdadero

, x = 30 W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

Verdadero

Las soluciones son

x = 30 W_{- 1} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}, x = 30 W_{0} (- \frac{1}{e ^{\frac{226}{225}}}) + \frac{452}{15}

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