7e^{3x}=8e^{5x}

Lösung

7 e^{3 x} = 8 e^{5 x}

x = - \frac{3 ln ( 2 ) - ln ( 7 )}{2}

Dezimale

x = - 0.06676 \dots

Schritte zur Lösung

7 e^{3 x} = 8 e^{5 x}

Wende Exponentenregel an

ln (7) + 3 x = ln (8) + 5 x

Löse

ln (7) + 3 x = ln (8) + 5 x : x = - \frac{3 ln ( 2 ) - ln ( 7 )}{2}

x = - \frac{3 ln ( 2 ) - ln ( 7 )}{2}

2^{x - 8} = 5

8^{x^{2} - 4} = 1

so l v e f or x, 2^{x - 9} = 9

6^{x - 1} - 2 = 62

so l v e f or x, (1.3)^{x} = 27