5^{x-2}*3^{2x-5}=675

Lösung

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

x = \frac{ln ( 675 ) + ln ( 6075 )}{ln ( 45 )}

Dezimale

x = 4

Schritte zur Lösung

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

Wende Exponentenregel an

(lo g_{3} (5) (x - 2) + 2 x - 5) ln (3) = ln (675)

Löse

(lo g_{3} (5) (x - 2) + 2 x - 5) ln (3) = ln (675) : x = \frac{ln ( 675 ) + ln ( 6075 )}{ln ( 45 )}

x = \frac{ln ( 675 ) + ln ( 6075 )}{ln ( 45 )}

2^{x} - 10 = 6

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

e^{x} = 10

8^{x} = 2

(\frac{9}{4})^{2 x} = \frac{81}{16}