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

Lösung

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

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

Dezimale

x = - 0.77321 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Löse

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

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

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

3^{x + 1} = 3^{x} + 18

3^{5 x + 2} = 9^{x + 4}

e^{k} = 4.5

ln (e^{2 x - 1}) = 5