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Beliebt Algebra >

solvefor x,e^{sqrt(t)}=x^6

Lösung

löse nach

x, e^{t} = x^{6}

Lösung

x = 6 e^{t}, x = - 6 e^{t}, x = \frac{3 3 e ^{t}}{4 - \frac{- 3 e ^{t} + 2 e ^{\frac{2}{3}}}{4}} + - \frac{- 3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{4} i, x = - \frac{3 3 e ^{t}}{4 - \frac{- 3 e ^{t} + 2 e ^{\frac{2}{3}}}{4}} - - \frac{- 3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{4} i, x = \frac{3 3 e ^{t}}{2 3 e ^{t} + 2 e ^{\frac{2 t}{3}}} + \frac{3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{2} i, x = - \frac{3 3 e ^{t}}{2 3 e ^{t} + 2 e ^{\frac{2 t}{3}}} - \frac{3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{2} i, x = - \frac{3 3 e ^{t}}{4 - \frac{- 3 e ^{t} + 2 e ^{\frac{2}{3}}}{4}} + - \frac{- 3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{4} i, x = \frac{3 3 e ^{t}}{4 - \frac{- 3 e ^{t} + 2 e ^{\frac{2}{3}}}{4}} - - \frac{- 3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{4} i, x = - \frac{3 3 e ^{t}}{2 3 e ^{t} + 2 e ^{\frac{2 t}{3}}} + \frac{3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{2} i, x = \frac{3 3 e ^{t}}{2 3 e ^{t} + 2 e ^{\frac{2 t}{3}}} - \frac{3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{2} i

Schritte zur Lösung

e^{t} = x^{6}

Tausche die Seiten

x^{6} = e^{t}

Schreibe die Gleichung um mit

u = x^{2}

und

u^{3} = x^{6}

u^{3} = e^{t}

Löse

u^{3} = e^{t} : u = 3 e^{t}, u = 3 e^{t} \frac{- 1 + 3 i}{2}, u = 3 e^{t} \frac{- 1 - 3 i}{2}

u = 3 e^{t}, u = 3 e^{t} \frac{- 1 + 3 i}{2}, u = 3 e^{t} \frac{- 1 - 3 i}{2}

Setze

u = x^{2} w i e d er e in,

löse für

x

Löse

x^{2} = 3 e^{t} : x = 6 e^{t}, x = - 6 e^{t}

Löse

x^{2} = 3 e^{t} \frac{- 1 + 3 i}{2} : x = \frac{3 3 e ^{t}}{4 - \frac{- 3 e ^{t} + 2 e ^{\frac{2}{3}}}{4}} + - \frac{- 3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{4} i, x = - \frac{3 3 e ^{t}}{4 - \frac{- 3 e ^{t} + 2 e ^{\frac{2}{3}}}{4}} - - \frac{- 3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{4} i, x = \frac{3 3 e ^{t}}{2 3 e ^{t} + 2 e ^{\frac{2 t}{3}}} + \frac{3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{2} i, x = - \frac{3 3 e ^{t}}{2 3 e ^{t} + 2 e ^{\frac{2 t}{3}}} - \frac{3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{2} i

Löse

x^{2} = 3 e^{t} \frac{- 1 - 3 i}{2} : x = - \frac{3 3 e ^{t}}{4 - \frac{- 3 e ^{t} + 2 e ^{\frac{2}{3}}}{4}} + - \frac{- 3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{4} i, x = \frac{3 3 e ^{t}}{4 - \frac{- 3 e ^{t} + 2 e ^{\frac{2}{3}}}{4}} - - \frac{- 3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{4} i, x = - \frac{3 3 e ^{t}}{2 3 e ^{t} + 2 e ^{\frac{2 t}{3}}} + \frac{3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{2} i, x = \frac{3 3 e ^{t}}{2 3 e ^{t} + 2 e ^{\frac{2 t}{3}}} - \frac{3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{2} i

Die Lösungen sind

x = 6 e^{t}, x = - 6 e^{t}, x = \frac{3 3 e ^{t}}{4 - \frac{- 3 e ^{t} + 2 e ^{\frac{2}{3}}}{4}} + - \frac{- 3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{4} i, x = - \frac{3 3 e ^{t}}{4 - \frac{- 3 e ^{t} + 2 e ^{\frac{2}{3}}}{4}} - - \frac{- 3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{4} i, x = \frac{3 3 e ^{t}}{2 3 e ^{t} + 2 e ^{\frac{2 t}{3}}} + \frac{3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{2} i, x = - \frac{3 3 e ^{t}}{2 3 e ^{t} + 2 e ^{\frac{2 t}{3}}} - \frac{3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{2} i, x = - \frac{3 3 e ^{t}}{4 - \frac{- 3 e ^{t} + 2 e ^{\frac{2}{3}}}{4}} + - \frac{- 3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{4} i, x = \frac{3 3 e ^{t}}{4 - \frac{- 3 e ^{t} + 2 e ^{\frac{2}{3}}}{4}} - - \frac{- 3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{4} i, x = - \frac{3 3 e ^{t}}{2 3 e ^{t} + 2 e ^{\frac{2 t}{3}}} + \frac{3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{2} i, x = \frac{3 3 e ^{t}}{2 3 e ^{t} + 2 e ^{\frac{2 t}{3}}} - \frac{3 e ^{t} + 2 e ^{\frac{2 t}{3}}}{2} i

Graph

Beliebte Beispiele

4x^3-36x^2-96x-64=0

4 x^{3} - 36 x^{2} - 96 x - 64 = 0

8 x^{3} - 8 = 0

solvefor x,x^3-y^4=3

so l v e f or x, x^{3} - y^{4} = 3

3 x^{4} = 375 x

(x^6)^7=(7.9)^{42}

(x^{6})^{7} = (7.9)^{42}