9^{x-1}=5^{2x-2}

Lösung

9^{x - 1} = 5^{2 x - 2}

x = - \frac{2 ln ( 5 ) - 2 ln ( 3 )}{2 ( ln ( 3 ) - ln ( 5 ) )}

Dezimale

x = 1

Schritte zur Lösung

9^{x - 1} = 5^{2 x - 2}

Wende Exponentenregel an

(x - 1) ln (9) = (2 x - 2) ln (5)

Löse

(x - 1) ln (9) = (2 x - 2) ln (5) : x = - \frac{2 ln ( 5 ) - 2 ln ( 3 )}{2 ( ln ( 3 ) - ln ( 5 ) )}

x = - \frac{2 ln ( 5 ) - 2 ln ( 3 )}{2 ( ln ( 3 ) - ln ( 5 ) )}

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

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

2 (9^{x}) - 7 (3^{x}) + 3 = 0

2^{2 x} + 2^{x} - 20 = 0

4^{x} - 2 \cdot 2^{x} + 12 = 0