9^x=2e^{x^2}

Lösung

9^{x} = 2 e^{x^{2}}

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

Dezimale

x = 1.81541 \dots, x = 0.38181 \dots

Schritte zur Lösung

9^{x} = 2 e^{x^{2}}

Wende Exponentenregel an

x ln (9) = ln (2) + x^{2}

Löse

x ln (9) = ln (2) + x^{2} : x = \frac{2 ln ( 3 ) + 4 ln ^{2} ( 3 ) - 4 ln ( 2 )}{2}, x = \frac{2 ln ( 3 ) - 4 ln ^{2} ( 3 ) - 4 ln ( 2 )}{2}

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

2^{x - 1} = 4

1 6^{x + 3} = 6 4^{2 x - 1}

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

2^{x} = 0.1

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