5^{2x-3}=7^{x-1}

Lösung

5^{2 x - 3} = 7^{x - 1}

x = \frac{- ln ( 7 ) + 3 ln ( 5 )}{2 ln ( 5 ) - ln ( 7 )}

Dezimale

x = 2.26432 \dots

Schritte zur Lösung

5^{2 x - 3} = 7^{x - 1}

Wende Exponentenregel an

(2 x - 3) ln (5) = (x - 1) ln (7)

Löse

(2 x - 3) ln (5) = (x - 1) ln (7) : x = \frac{- ln ( 7 ) + 3 ln ( 5 )}{2 ln ( 5 ) - ln ( 7 )}

x = \frac{- ln ( 7 ) + 3 ln ( 5 )}{2 ln ( 5 ) - ln ( 7 )}

ln (e^{5 x}) + ln (4) = 6

e^{2 x} - 11 e^{x} + 28 = 0

4^{x + 2} = 8^{- 2 x}

3^{x} e^{4 x} = e^{7}

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