8^{2x-1}=3^{x-2}

Lösung

8^{2 x - 1} = 3^{x - 2}

x = \frac{- 2 ln ( 3 ) + 3 ln ( 2 )}{6 ln ( 2 ) - ln ( 3 )}

Dezimale

x = - 0.03848 \dots

Schritte zur Lösung

8^{2 x - 1} = 3^{x - 2}

Wende Exponentenregel an

(2 x - 1) ln (8) = (x - 2) ln (3)

Löse

(2 x - 1) ln (8) = (x - 2) ln (3) : x = \frac{- 2 ln ( 3 ) + 3 ln ( 2 )}{6 ln ( 2 ) - ln ( 3 )}

x = \frac{- 2 ln ( 3 ) + 3 ln ( 2 )}{6 ln ( 2 ) - ln ( 3 )}

3^{2 x + 1} - 4 (3^{3 x + 1}) + 1 = 0

1 0^{x} = 10

1 0^{x} = 24

x \cdot e^{x} = 1

8^{3 x - 1} = 4^{3 - 2 x}