5^{x+2}=4^{2x-1}

Lösung

5^{x + 2} = 4^{2 x - 1}

x = \frac{2 ln ( 10 )}{4 ln ( 2 ) - ln ( 5 )}

Dezimale

x = 3.95922 \dots

Schritte zur Lösung

5^{x + 2} = 4^{2 x - 1}

Wende Exponentenregel an

(x + 2) ln (5) = (2 x - 1) ln (4)

Löse

(x + 2) ln (5) = (2 x - 1) ln (4) : x = \frac{2 ln ( 10 )}{4 ln ( 2 ) - ln ( 5 )}

x = \frac{2 ln ( 10 )}{4 ln ( 2 ) - ln ( 5 )}

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

e^{e} - 12 e^{- x} - 1 = 0

5 = 10 (0.8)^{x}

2 7^{x} = 9^{x - 4}

5. 3^{x} + 2. 3^{3} = 63