(5/7)^{-5}*(5/7)^{3x}=(1/3)^{-2}

Lösung

(\frac{5}{7})^{- 5} \cdot (\frac{5}{7})^{3 x} = (\frac{1}{3})^{- 2}

x = \frac{ln ( \frac{28125}{16807} )}{3 ln ( \frac{5}{7} )}

Dezimale

x = - 0.51006 \dots

Schritte zur Lösung

(\frac{5}{7})^{- 5} (\frac{5}{7})^{3 x} = (\frac{1}{3})^{- 2}

Wende Exponentenregel an

(3 x - 5) ln (\frac{5}{7}) = - 2 ln (\frac{1}{3})

Löse

(3 x - 5) ln (\frac{5}{7}) = - 2 ln (\frac{1}{3}) : x = \frac{ln ( \frac{28125}{16807} )}{3 ln ( \frac{5}{7} )}

x = \frac{ln ( \frac{28125}{16807} )}{3 ln ( \frac{5}{7} )}

7^{x} = - 7

5^{x - 2} \cdot 3^{2 x - 5} = 675

2^{x} - 10 = 6

so l v e f or p, 2^{p - 1} + 5 = 3^{q}

e^{x} = 10