3^x=x^4

Lösung

3^{x} = x^{4}

x = - \frac{4 W _{0} ( \frac{l n ( 3 )}{4} )}{ln ( 3 )}, x = - \frac{4 W _{0} ( - \frac{l n ( 3 )}{4} )}{ln ( 3 )}, x = - \frac{4 W _{- 1} ( - \frac{l n ( 3 )}{4} )}{ln ( 3 )}

Dezimale

x = - 0.80224 \dots, x = 1.51677 \dots, x = 7.17475 \dots

Schritte zur Lösung

3^{x} = x^{4}

Potenziere beide Seiten der Gleichung mit

\frac{1}{4}

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

Vereinfache

(3^{x})^{\frac{1}{4}} : 3^{\frac{x}{4}}

Vereinfache

(x^{4})^{\frac{1}{4}} : ∣ x ∣

Löse

3^{\frac{x}{4}} = ∣ x ∣ : x = - \frac{4 W _{0} ( \frac{l n ( 3 )}{4} )}{ln ( 3 )} or x = - \frac{4 W _{0} ( - \frac{l n ( 3 )}{4} )}{ln ( 3 )} or x = - \frac{4 W _{- 1} ( - \frac{l n ( 3 )}{4} )}{ln ( 3 )}

x = - \frac{4 W _{0} ( \frac{l n ( 3 )}{4} )}{ln ( 3 )}, x = - \frac{4 W _{0} ( - \frac{l n ( 3 )}{4} )}{ln ( 3 )}, x = - \frac{4 W _{- 1} ( - \frac{l n ( 3 )}{4} )}{ln ( 3 )}

so l v e f or x, 0 = 2 e^{- x} x + (- e^{- x}) x^{2}

2^{x} = 134217728

24 3^{2} = 9^{x + 2}

\frac{5 ^{x^{2} + 1}}{2 5 ^{x + 2}} = 3125

e^{2 x} - 5 e^{x} = 0