x^{10}=2^x

Lösung

x^{10} = 2^{x}

x = - \frac{10 W _{0} ( \frac{l n ( 2 )}{10} )}{ln ( 2 )}, x = - \frac{10 W _{0} ( - \frac{l n ( 2 )}{10} )}{ln ( 2 )}, x = - \frac{10 W _{- 1} ( - \frac{l n ( 2 )}{10} )}{ln ( 2 )}

Dezimale

x = - 0.93710 \dots, x = 1.07755 \dots, x = 58.77010 \dots

Schritte zur Lösung

x^{10} = 2^{x}

Potenziere beide Seiten der Gleichung mit

\frac{1}{10}

(x^{10})^{\frac{1}{10}} = (2^{x})^{\frac{1}{10}}

Vereinfache

(x^{10})^{\frac{1}{10}} : ∣ x ∣

Vereinfache

(2^{x})^{\frac{1}{10}} : 2^{\frac{x}{10}}

Löse

∣ x ∣ = 2^{\frac{x}{10}} : x = - \frac{10 W _{0} ( \frac{l n ( 2 )}{10} )}{ln ( 2 )} or x = - \frac{10 W _{0} ( - \frac{l n ( 2 )}{10} )}{ln ( 2 )} or x = - \frac{10 W _{- 1} ( - \frac{l n ( 2 )}{10} )}{ln ( 2 )}

x = - \frac{10 W _{0} ( \frac{l n ( 2 )}{10} )}{ln ( 2 )}, x = - \frac{10 W _{0} ( - \frac{l n ( 2 )}{10} )}{ln ( 2 )}, x = - \frac{10 W _{- 1} ( - \frac{l n ( 2 )}{10} )}{ln ( 2 )}

8^{5 x - 7} = 9^{2 x - 3}

0.2 = (\frac{4}{5})^{x}

2^{x + 2} - 3 x (2^{x - 1}) = 20

(1 + x) \cdot 4 = 2^{x}

x + 1 100 = 1