sqrt(5^{4x+2)}=7^{x+5}

Lösung

5^{4 x + 2} = 7^{x + 5}

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

Dezimale

x = 6.37889 \dots

Schritte zur Lösung

5^{4 x + 2} = 7^{x + 5}

Wende Exponentenregel an

(4 x + 2) \frac{1}{2} ln (5) = (x + 5) ln (7)

Löse

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

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

2^{2 x} + 2^{x + 2} = 32

9^{x} - 16 \cdot 3^{x} + 27 = 0

3 e^{x} - x e^{x} = 0

2 5^{2 x + 1} - 1 = 143

11 (1 + e^{- x})^{- 1} = 3