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14.47=(x-11)/(ln(x/(11)))

Solución

14.47 = \frac{x - 11}{ln ( \frac{x}{11} )}

Solución

x = - \frac{1447 W _{- 1} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}

+1

Decimal

x = 18.60271 \dots

Pasos de solución

14.47 = \frac{x - 11}{ln ( \frac{x}{11} )}

Multiplicar ambos lados por

ln (\frac{x}{11})

14.47 ln (\frac{x}{11}) = x - 11

Multiplicar ambos lados por

100

1447 ln (\frac{x}{11}) = 100 x - 1100

Dividir ambos lados entre

1447

ln (\frac{x}{11}) = \frac{100 x - 1100}{1447}

Si

f (x) = g (x),

entonces

a^{f (x)} = a^{g (x)}

e^{l n (\frac{x}{11})} = e^{\frac{100 x - 1100}{1447}}

Simplificar

e^{l n (\frac{x}{11})} : \frac{x}{11}

\frac{x}{11} = e^{\frac{100 x - 1100}{1447}}

Multiplicar ambos lados por

11

\frac{x}{11} \cdot 11 = e^{\frac{100 x - 1100}{1447}} \cdot 11

Simplificar

x = e^{\frac{100 x - 1100}{1447}} \cdot 11

Resolver

x = e^{\frac{100 x - 1100}{1447}} \cdot 11 : x = - \frac{1447 W _{- 1} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}, x = - \frac{1447 W _{0} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}

x = - \frac{1447 W _{- 1} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}, x = - \frac{1447 W _{0} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}

Verificar las soluciones:

x = - \frac{1447 W _{- 1} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}

Verdadero

, x = - \frac{1447 W _{0} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}

Falso

La solución es

x = - \frac{1447 W _{- 1} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}

Gráfica

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