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

Lösung

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

x = \frac{ln ( 15 )}{3 ln ( 5 ) - 2 ln ( 3 )}

Dezimale

x = 1.02925 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Löse

(2 x + 1) ln (3) = (3 x - 1) ln (5) : x = \frac{ln ( 15 )}{3 ln ( 5 ) - 2 ln ( 3 )}

x = \frac{ln ( 15 )}{3 ln ( 5 ) - 2 ln ( 3 )}

\frac{200}{335} = e^{15 x}

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

6640 = 5000 (1 + 0.001)^{T}

e^{x} = 2 x + 1

e^{x} = 2 x + 2