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

Lösung

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

x = \frac{- 1 + 4 ln ( 5 ) - 3}{2}, x = \frac{- 1 - 4 ln ( 5 ) - 3}{2}

Dezimale

x = 0.42705 \dots, x = - 1.42705 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

x^{2} + 1 = ln (5) - x

Löse

x^{2} + 1 = ln (5) - x : x = \frac{- 1 + 4 ln ( 5 ) - 3}{2}, x = \frac{- 1 - 4 ln ( 5 ) - 3}{2}

x = \frac{- 1 + 4 ln ( 5 ) - 3}{2}, x = \frac{- 1 - 4 ln ( 5 ) - 3}{2}

x^{5} = 5^{x}

4^{x + 1} = 64

2^{2 x + 1} = 4

e^{x} = - 3

(\frac{1}{4})^{4 x} = 0.25