7^{2x+4}=3^{5x+7}

Lösung

7^{2 x + 4} = 3^{5 x + 7}

x = \frac{4 ln ( 7 ) - 7 ln ( 3 )}{5 ln ( 3 ) - 2 ln ( 7 )}

Dezimale

x = 0.05830 \dots

Schritte zur Lösung

7^{2 x + 4} = 3^{5 x + 7}

Wende Exponentenregel an

(2 x + 4) ln (7) = (5 x + 7) ln (3)

Löse

(2 x + 4) ln (7) = (5 x + 7) ln (3) : x = \frac{4 ln ( 7 ) - 7 ln ( 3 )}{5 ln ( 3 ) - 2 ln ( 7 )}

x = \frac{4 ln ( 7 ) - 7 ln ( 3 )}{5 ln ( 3 ) - 2 ln ( 7 )}

4^{x^{2}} \cdot 4^{x} = 4^{0}

4^{x + 1} - 7 (2^{x}) = 2

so l v e f or x, 2^{π + 3 x} = 4^{2 y + 1}

5^{\frac{1}{t}} = 30

7^{5 x - 5} = 1