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Beliebt Algebra >

2^x=x^4

Lösung

2^{x} = x^{4}

Lösung

x = - \frac{4 W _{0} ( \frac{l n ( 2 )}{4} )}{ln ( 2 )}, x = - \frac{4 W _{0} ( - \frac{l n ( 2 )}{4} )}{ln ( 2 )}, x = 16

+1

Dezimale

x = - 0.86134 \dots, x = 1.23962 \dots, x = 16

Schritte zur Lösung

2^{x} = x^{4}

Potenziere beide Seiten der Gleichung mit

\frac{1}{4}

(2^{x})^{\frac{1}{4}} = (x^{4})^{\frac{1}{4}}

Vereinfache

(2^{x})^{\frac{1}{4}} : 2^{\frac{x}{4}}

Vereinfache

(x^{4})^{\frac{1}{4}} : ∣ x ∣

Löse

2^{\frac{x}{4}} = ∣ x ∣ : x = - \frac{4 W _{0} ( \frac{l n ( 2 )}{4} )}{ln ( 2 )} or x = - \frac{4 W _{0} ( - \frac{l n ( 2 )}{4} )}{ln ( 2 )} or x = 16

x = - \frac{4 W _{0} ( \frac{l n ( 2 )}{4} )}{ln ( 2 )}, x = - \frac{4 W _{0} ( - \frac{l n ( 2 )}{4} )}{ln ( 2 )}, x = 16

Graph

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