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

Lösung

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

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

Dezimale

x = 0.75907 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Löse

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

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