e^{x^2}=e^x(e^{x-1})^2

Lösung

e^{x^{2}} = e^{x} (e^{x - 1})^{2}

x = 2, x = 1

Schritte zur Lösung

e^{x^{2}} = e^{x} (e^{x - 1})^{2}

Wende Exponentenregel an

x^{2} = x + (x - 1) \cdot 2

Löse

x^{2} = x + (x - 1) \cdot 2 : x = 2, x = 1

x = 2, x = 1

\frac{1}{2 ^{x}} = 8

2^{2 x} - 3 \cdot 2^{2 x} + 2 = 0

9^{6 - x} = 3^{2 x - 4}

2 (e^{x}) + e^{x} = 0

3^{4 x + 1} \cdot 9^{x - 1} = 81