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

Lösung

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

x = \frac{ln ( 15 )}{ln ( 5 ) - 2 ln ( 3 )}

Dezimale

x = - 4.60719 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

(x - 1) ln (5) = (2 x + 1) ln (3)

Löse

(x - 1) ln (5) = (2 x + 1) ln (3) : x = \frac{ln ( 15 )}{ln ( 5 ) - 2 ln ( 3 )}

x = \frac{ln ( 15 )}{ln ( 5 ) - 2 ln ( 3 )}

201 \cdot 2^{x} = 67

4^{5 x + 1} = 16

8^{x - 1} = \frac{1}{16 2}

\frac{32}{8 16} = 2^{x}

2^{x + 3} - 2^{x + 1} = 12