5^{x^2}=25^{x+1}

Lösung

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

x = 1 + 3, x = 1 - 3

Dezimale

x = 2.73205 \dots, x = - 0.73205 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

x^{2} = 2 (x + 1)

Löse

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

x = 1 + 3, x = 1 - 3

5^{2 x} - 5^{x + 1} + 4 = 0

3^{x + 1} + 4 = 8

so l v e f or n, 4^{n + 1} = 8^{n - 2}

2^{2 x + 11} = 3^{x - 5}

(\frac{2}{5})^{x} = \frac{4}{25}