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

Lösung

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

x = \frac{ln ( 72 )}{ln ( 48 )}

Dezimale

x = 1.10473 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Löse

(4 x - 3) ln (2) = (2 - x) ln (3) : x = \frac{ln ( 72 )}{ln ( 48 )}

x = \frac{ln ( 72 )}{ln ( 48 )}

3^{2 x} - 4 \times 3^{x} + 3 = 0

10 \cdot 3^{x + 3} = 60

3^{x} = 64

2^{x - 3} = 8

2^{3 x + 2} - 2^{3 x - 2} = 30