2^x=3^{x+1}

Lösung

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

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

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 ( 2 ) - ln ( 3 )}

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

2^{x} \cdot 2^{4} = 2^{2 x}

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

5^{2 x^{2} - 3 x - 2} = 1

8^{x} = 16

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