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

Lösung

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

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

Dezimale

x = - 2.73813 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

2 x ln (3) = (x - 1) ln (5)

Löse

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

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

e^{\frac{1}{x}} = 0

x^{x^{9}} = 3^{3}

- e^{- x} = 0

3 2^{\frac{x}{3}} = 8^{x - 12}

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