2sqrt(2)=e^{x-3}+e^{-(x-3)}

Lösung

22 = e^{x - 3} + e^{- (x - 3)}

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

Dezimale

x = 3.88137 \dots, x = 2.11862 \dots

Schritte zur Lösung

22 = e^{x - 3} + e^{- (x - 3)}

Wende Exponentenregel an

22 = e^{x} e^{- 3} + (e^{x})^{- 1} e^{3}

Schreibe die Gleichung um mit

e^{x} = u

22 = u e^{- 3} + (u)^{- 1} e^{3}

Löse

22 = u e^{- 3} + u^{- 1} e^{3} : u = e^{3} (1 + 2), u = e^{3} (2 - 1)

u = e^{3} (1 + 2), u = e^{3} (2 - 1)

Setze

u = e^{x} w i e d er e in,

löse für

x

Löse

e^{x} = e^{3} (1 + 2) : x = ln (1 + 2) + 3

Löse

e^{x} = e^{3} (2 - 1) : x = ln (2 - 1) + 3

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

4665 6^{2 x - 6} = 3 6^{x - 12}

4^{(2 x - 5)} = 64

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

so l v e f or x, z = x e^{x y}

m 3^{7} = 3