8^{5x-7}=9^{2x-3}

Lösung

8^{5 x - 7} = 9^{2 x - 3}

x = \frac{- 6 ln ( 3 ) + 21 ln ( 2 )}{15 ln ( 2 ) - 4 ln ( 3 )}

Dezimale

x = 1.32679 \dots

Schritte zur Lösung

8^{5 x - 7} = 9^{2 x - 3}

Wende Exponentenregel an

(5 x - 7) ln (8) = (2 x - 3) ln (9)

Löse

(5 x - 7) ln (8) = (2 x - 3) ln (9) : x = \frac{- 6 ln ( 3 ) + 21 ln ( 2 )}{15 ln ( 2 ) - 4 ln ( 3 )}

x = \frac{- 6 ln ( 3 ) + 21 ln ( 2 )}{15 ln ( 2 ) - 4 ln ( 3 )}

0.2 = (\frac{4}{5})^{x}

2^{x + 2} - 3 x (2^{x - 1}) = 20

(1 + x) \cdot 4 = 2^{x}

x + 1 100 = 1

5^{t} = 7