(6^2)(2^{2x-3})=16^{x-2}

Lösung

(6^{2}) (2^{2 x - 3}) = 1 6^{x - 2}

x = \frac{ln ( 1152 )}{2 ln ( 2 )}

Dezimale

x = 5.08496 \dots

Schritte zur Lösung

(6^{2}) (2^{2 x - 3}) = 1 6^{x - 2}

Wende Exponentenregel an

ln (6^{2}) + (2 x - 3) ln (2) = 4 (x - 2) ln (2)

Löse

ln (6^{2}) + (2 x - 3) ln (2) = 4 (x - 2) ln (2) : x = \frac{ln ( 1152 )}{2 ln ( 2 )}

x = \frac{ln ( 1152 )}{2 ln ( 2 )}

8^{x} = 2^{6}

2^{x - 1} = 500000

4^{2 x + 1} = 16

(3^{3})^{x} = 27

1 0^{2 x - 1} = - 10