3^x5^{x+1}=12^{x-1}

Lösung

3^{x} 5^{x + 1} = 1 2^{x - 1}

x = - \frac{ln ( 60 )}{ln ( \frac{5}{4} )}

Dezimale

x = - 18.34847 \dots

Schritte zur Lösung

3^{x} \cdot 5^{x + 1} = 1 2^{x - 1}

Wende Exponentenregel an

x ln (15) + ln (5^{1}) = (x - 1) ln (12)

Löse

x ln (15) + ln (5^{1}) = (x - 1) ln (12) : x = - \frac{ln ( 60 )}{ln ( \frac{5}{4} )}

x = - \frac{ln ( 60 )}{ln ( \frac{5}{4} )}

3^{2 x} = - 81

- 5 e^{- 5 x} = 0

e^{x} - 8 = 0

9^{x} = 10

5^{7 x + 5} = 2