8^{x^2}=9^x

Lösung

8^{x^{2}} = 9^{x}

x = 0, x = \frac{2 ln ( 3 )}{3 ln ( 2 )}

Dezimale

x = 0, x = 1.05664 \dots

Schritte zur Lösung

8^{x^{2}} = 9^{x}

Wende Exponentenregel an

x^{2} ln (8) = x ln (9)

Löse

x^{2} ln (8) = x ln (9) : x = 0, x = \frac{2 ln ( 3 )}{3 ln ( 2 )}

x = 0, x = \frac{2 ln ( 3 )}{3 ln ( 2 )}

so l v e f or θ, r = φ e^{- θ} + ω θ e^{- θ}

3^{x} = 81

6^{x} = 38

6^{x} = 15

5^{2 x + 1} = 3125