7^{2x+1}=3^{x+2}

Lösung

7^{2 x + 1} = 3^{x + 2}

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

Dezimale

x = 0.08997 \dots

Schritte zur Lösung

7^{2 x + 1} = 3^{x + 2}

Wende Exponentenregel an

(2 x + 1) ln (7) = (x + 2) ln (3)

Löse

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

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

e^{6 x} = 6 e^{x}

so l v e f or t, x = e^{- t}

3^{x} \cdot 3^{x + 1} = 9

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

4 = 1.0 5^{x}