solvefor x,4e^{2x+3}=7e^{3x-2}

Lösung

löse nach

x, 4 e^{2 x + 3} = 7 e^{3 x - 2}

x = 2 ln (2) + 5 - ln (7)

Dezimale

x = 4.44038 \dots

Schritte zur Lösung

4 e^{2 x + 3} = 7 e^{3 x - 2}

Wende Exponentenregel an

ln (4) + 2 x + 3 = ln (7) + 3 x - 2

Löse

ln (4) + 2 x + 3 = ln (7) + 3 x - 2 : x = 2 ln (2) + 5 - ln (7)

x = 2 ln (2) + 5 - ln (7)

5^{x} = 87

4^{2 x} = 3 2^{\frac{1}{2}}

5^{2 x} - 5^{x} + 1 = 0

(\frac{1}{2})^{x - 1} = 32

4^{2 x + 5} = 64