2^{x^2-2x}=3

Lösung

2^{x^{2} - 2 x} = 3

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

Dezimale

x = 2.60778 \dots, x = - 0.60778 \dots

Schritte zur Lösung

2^{x^{2} - 2 x} = 3

Wende Exponentenregel an

(x^{2} - 2 x) ln (2) = ln (3)

Löse

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

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

4^{x} + 2^{x} = 72

so l v e f or j, y = \frac{1}{( 2 ^{j} )}

2 \cdot 3^{x} + 1 = 10. 3^{12} \cdot 8. 3^{12}

9 = 3^{m}

\frac{2 ^{x} + 1}{( 2 ^{x} )} = \frac{41}{4}