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

Lösung

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

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

Dezimale

x = 7.51778 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Löse

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

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

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

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

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

so l v e f or x, 7^{5 x + 7} = 2

3 8 1^{x} = \frac{1}{27}