5^{x+2}=7^{2x+1}

Lösung

5^{x + 2} = 7^{2 x + 1}

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

Dezimale

x = 0.55773 \dots

Schritte zur Lösung

5^{x + 2} = 7^{2 x + 1}

Wende Exponentenregel an

(x + 2) ln (5) = (2 x + 1) ln (7)

Löse

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

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

4^{x + 6} = 7

4^{3 x + 5} = 16

5^{1 - 2 x} = \frac{1}{5}

4^{x + 2} + 8 \cdot 2^{x + 2} = 128

1 6^{3 - x} = (\frac{1}{2})^{2 x + 4}