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

Lösung

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

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

Dezimale

x = - 14.27491 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Löse

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

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

2^{x + 2} - 2^{x + 5} + 7 = 0

95 = 2 7^{x}

2^{2 x - 5} = 16

2 (\frac{1}{8})^{1 - 2 x} = 1 6^{x + 6}

2 = 2^{x}