3^{2(x-1)}=2^{x-3}

Lösung

3^{2 (x - 1)} = 2^{x - 3}

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

Dezimale

x = 0.07830 \dots

Schritte zur Lösung

3^{2 (x - 1)} = 2^{x - 3}

Wende Exponentenregel an

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

Löse

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

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

51 e^{x} = 510

9^{x + 3} = 24 3^{3 - x}

4 e^{x} = 18

5^{2 x - 1} = 2 (3^{x})

3^{2 x} + 9^{x} = 162