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

解

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 )}

十進法表記

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

解答ステップ

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

指数の規則を適用する

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

解く

(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 )}