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

Lösung

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

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

Dezimale

x = - 3.21163 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Löse

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

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

3^{2 x} = 9

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

2^{x - 1} = 1

81 = 3^{x}

3^{2 x} = 27