5^{2x-3}=3^{3x+4}

Lösung

5^{2 x - 3} = 3^{3 x + 4}

x = \frac{4 ln ( 3 ) + 3 ln ( 5 )}{2 ln ( 5 ) - 3 ln ( 3 )}

Dezimale

x = - 119.83677 \dots

Schritte zur Lösung

5^{2 x - 3} = 3^{3 x + 4}

Wende Exponentenregel an

(2 x - 3) ln (5) = (3 x + 4) ln (3)

Löse

(2 x - 3) ln (5) = (3 x + 4) ln (3) : x = \frac{4 ln ( 3 ) + 3 ln ( 5 )}{2 ln ( 5 ) - 3 ln ( 3 )}

x = \frac{4 ln ( 3 ) + 3 ln ( 5 )}{2 ln ( 5 ) - 3 ln ( 3 )}