2^x=3^{x-1}

Lösung

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

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

Dezimale

x = 2.70951 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Löse

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

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

3^{3 x - 2} = 81

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

3^{x} = 7

4 e^{2 x} - 7 e^{x} = 15

2^{2 x} - 5 \cdot 2^{x} + 6 = 0