2^x=x^{100}

Lösung

2^{x} = x^{100}

x = - \frac{100 W _{0} ( \frac{l n ( 2 )}{100} )}{ln ( 2 )}, x = - \frac{100 W _{0} ( - \frac{l n ( 2 )}{100} )}{ln ( 2 )}, x = - \frac{100 W _{- 1} ( - \frac{l n ( 2 )}{100} )}{ln ( 2 )}

Dezimale

x = - 0.99313 \dots, x = 1.00700 \dots, x = 996.00022 \dots

Schritte zur Lösung

2^{x} = x^{100}

Potenziere beide Seiten der Gleichung mit

\frac{1}{100}

(2^{x})^{\frac{1}{100}} = (x^{100})^{\frac{1}{100}}

Vereinfache

(2^{x})^{\frac{1}{100}} : 2^{\frac{x}{100}}

Vereinfache

(x^{100})^{\frac{1}{100}} : ∣ x ∣

Löse

2^{\frac{x}{100}} = ∣ x ∣ : x = - \frac{100 W _{0} ( \frac{l n ( 2 )}{100} )}{ln ( 2 )} or x = - \frac{100 W _{0} ( - \frac{l n ( 2 )}{100} )}{ln ( 2 )} or x = - \frac{100 W _{- 1} ( - \frac{l n ( 2 )}{100} )}{ln ( 2 )}

x = - \frac{100 W _{0} ( \frac{l n ( 2 )}{100} )}{ln ( 2 )}, x = - \frac{100 W _{0} ( - \frac{l n ( 2 )}{100} )}{ln ( 2 )}, x = - \frac{100 W _{- 1} ( - \frac{l n ( 2 )}{100} )}{ln ( 2 )}

lo g_{2} (16) = 8 \cdot 2^{- x}

100 \cdot 2^{4 x} = 15

so l v e f or x, e^{x y} = 0

3 e^{4 x + 1} = 2

9^{3 x + 2} = \frac{1}{3 ^{2 x - 5}}