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Popular >

x^x=\sqrt[4]{0.5}

Solución

Solución

x = \frac{1}{16}, x = \frac{ln ( 0.5 )}{4 W _{0} ( \frac{l n ( 0.5 )}{4} )}

+1

Notación decimal

x = 0.0625, x = 0.80669 \dots

Pasos de solución

Preparar

para la forma de Lambert:

x e^{- \frac{l n ( 0.5 )}{4 x}} = 1

Re-escribir la ecuación con

\frac{ln ( 0.5 )}{4 x} = u

y

x = \frac{ln ( 0.5 )}{4 u}

(\frac{ln ( 0.5 )}{4 u}) e^{- u} = 1

Reescribir

(\frac{ln ( 0.5 )}{4 u}) e^{- u} = 1

en forma de Lambert:

e^{u} u = \frac{ln ( 0.5 )}{4}

Resolver

e^{u} u = \frac{ln ( 0.5 )}{4} : u = 4 ln (0.5), u = W_{0} (\frac{ln ( 0.5 )}{4})

Verificar las soluciones:

u = 4 ln (0.5)

Verdadero

, u = W_{0} (\frac{ln ( 0.5 )}{4})

Verdadero

Las soluciones son

u = 4 ln (0.5), u = W_{0} (\frac{ln ( 0.5 )}{4})

Sustituir hacia atrás la

u = \frac{ln ( 0.5 )}{4 x},

resolver para

x

Resolver

\frac{ln ( 0.5 )}{4 x} = 4 ln (0.5) : x = \frac{1}{16}

Resolver

\frac{ln ( 0.5 )}{4 x} = W_{0} (\frac{ln ( 0.5 )}{4}) : x = \frac{ln ( 0.5 )}{4 W _{0} ( \frac{l n ( 0.5 )}{4} )}

x = \frac{1}{16}, x = \frac{ln ( 0.5 )}{4 W _{0} ( \frac{l n ( 0.5 )}{4} )}

Ejemplos populares

0 = e^{x} + x e^{x}

3^{x} = 2187

12=200(1-e^{-1/800 t})

12 = 200 (1 - e^{- \frac{1}{800} t})

7 = 5 e^{0.2 x}

731093=525600e^{0.03t}

731093 = 525600 e^{0.03 t}