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Popular >

x^{sqrt(x)}=10

Solución

x^{x} = 10

Solución

x = \frac{ln ^{2} ( 10 )}{4 W _{0} ( \frac{l n ( 10 )}{2} ) ^{2}}

+1

Notación decimal

x = 3.45276 \dots

Pasos de solución

x^{x} = 10

Preparar

x^{x} = 10

para la forma de Lambert:

x e^{- \frac{l n ( 10 )}{x}} = 1

Re-escribir la ecuación con

\frac{ln ( 10 )}{x} = u

y

x = \frac{ln ^{2} ( 10 )}{u ^{2}}

(\frac{ln ^{2} ( 10 )}{u ^{2}}) e^{- u} = 1

Resolver

(\frac{ln ^{2} ( 10 )}{u ^{2}}) e^{- u} = 1 : u = 2 W_{0} (\frac{ln ( 10 )}{2})

u = 2 W_{0} (\frac{ln ( 10 )}{2})

Sustituir hacia atrás la

u = \frac{ln ( 10 )}{x},

resolver para

x

Resolver

\frac{ln ( 10 )}{x} = 2 W_{0} (\frac{ln ( 10 )}{2}) : x = \frac{ln ^{2} ( 10 )}{4 W _{0} ( \frac{l n ( 10 )}{2} ) ^{2}}

x = \frac{ln ^{2} ( 10 )}{4 W _{0} ( \frac{l n ( 10 )}{2} ) ^{2}}

Verificar las soluciones:

x = \frac{ln ^{2} ( 10 )}{4 W _{0} ( \frac{l n ( 10 )}{2} ) ^{2}}

Verdadero

La solución es

x = \frac{ln ^{2} ( 10 )}{4 W _{0} ( \frac{l n ( 10 )}{2} ) ^{2}}

Verificar las soluciones:

x = \frac{ln ^{2} ( 10 )}{4 W _{0} ( \frac{l n ( 10 )}{2} ) ^{2}}

Verdadero

La solución es

x = \frac{ln ^{2} ( 10 )}{4 W _{0} ( \frac{l n ( 10 )}{2} ) ^{2}}

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