9^{4x-5}=25^{6x+2}

Lösung

9^{4 x - 5} = 2 5^{6 x + 2}

x = \frac{4 ln ( 5 ) + 10 ln ( 3 )}{4 ( 2 ln ( 3 ) - 3 ln ( 5 ) )}

Dezimale

x = - 1.65557 \dots

Schritte zur Lösung

9^{4 x - 5} = 2 5^{6 x + 2}

Wende Exponentenregel an

(4 x - 5) ln (9) = (6 x + 2) ln (25)

Löse

(4 x - 5) ln (9) = (6 x + 2) ln (25) : x = \frac{4 ln ( 5 ) + 10 ln ( 3 )}{4 ( 2 ln ( 3 ) - 3 ln ( 5 ) )}

x = \frac{4 ln ( 5 ) + 10 ln ( 3 )}{4 ( 2 ln ( 3 ) - 3 ln ( 5 ) )}

4^{3 + x} = 7^{1 - x}

4^{3 - x} = 4

\frac{1}{2} e^{x - 1} = 15

3^{x + 2} = 27

so l v e f or n, y^{n} + y = 0