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

Lösung

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

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

Dezimale

x = 5.60719 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Löse

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

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

7^{3 x - 2} = 1 3^{x + 1}

5^{(2 x)} - 6 (5^{x}) + 5 = 0

so l v e f or I, x = e^{I n (7)}

0.1 e^{0.1 x} = 0.5

5 = 1000 (1 - \frac{1}{3})^{x}