es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Álgebra >

e^{x^x}=2

Solución

e^{x^{x}} = 2

Solución

x = \frac{ln ( ln ( 2 ) )}{W _{- 1} ( ln ( ln ( 2 ) ) )}, x = \frac{ln ( ln ( 2 ) )}{W _{0} ( ln ( ln ( 2 ) ) )}

+1

Decimal

x = 0.33662 \dots, x = 0.40004 \dots

Pasos de solución

e^{x^{x}} = 2

Preparar

e^{x^{x}} = 2

para la forma de Lambert:

x e^{- \frac{l n ( l n ( 2 ) )}{x}} = 1

Re-escribir la ecuación con

\frac{ln ( ln ( 2 ) )}{x} = u

y

x = \frac{ln ( ln ( 2 ) )}{u}

(\frac{ln ( ln ( 2 ) )}{u}) e^{- u} = 1

Reescribir

(\frac{ln ( ln ( 2 ) )}{u}) e^{- u} = 1

en forma de Lambert:

u e^{u} = ln (ln (2))

Resolver

u e^{u} = ln (ln (2)) : u = W_{- 1} (ln (ln (2))), u = W_{0} (ln (ln (2)))

Verificar las soluciones:

u = W_{- 1} (ln (ln (2)))

Verdadero

, u = W_{0} (ln (ln (2)))

Verdadero

Las soluciones son

u = W_{- 1} (ln (ln (2))), u = W_{0} (ln (ln (2)))

Sustituir hacia atrás la

u = \frac{ln ( ln ( 2 ) )}{x},

resolver para

x

Resolver

\frac{ln ( ln ( 2 ) )}{x} = W_{- 1} (ln (ln (2))) : x = \frac{ln ( ln ( 2 ) )}{W _{- 1} ( ln ( ln ( 2 ) ) )}

Resolver

\frac{ln ( ln ( 2 ) )}{x} = W_{0} (ln (ln (2))) : x = \frac{ln ( ln ( 2 ) )}{W _{0} ( ln ( ln ( 2 ) ) )}

x = \frac{ln ( ln ( 2 ) )}{W _{- 1} ( ln ( ln ( 2 ) ) )}, x = \frac{ln ( ln ( 2 ) )}{W _{0} ( ln ( ln ( 2 ) ) )}

Gráfica

Ejemplos populares

3^{x+1}*2^{x+1}=36

7^{2x}+7^x-42=0

3^x-3^{-x}= 728/27

7^{3x+4}=49^{2x+1}