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

Lösung

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

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

Dezimale

x = 3.95922 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Löse

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

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

e^{(2 x)} - 2 e^{(x)} - 24 = 0

25 6^{- 1} = 1 6^{2 x - 2}

so l v e f or x, 2^{x} 3^{y} = 6

3 \cdot 5^{2 t - 1} = 75

4 \cdot 2^{- \frac{t}{5}} = 288