2^x*3^{x^2}=6

解

2^{x} \cdot 3^{x^{2}} = 6

x = \frac{- ln ( 2 ) + ln ^{2} ( 2 ) + 4 ln ( 3 ) ln ( 6 )}{2 ln ( 3 )}, x = \frac{- ln ( 2 ) - ln ^{2} ( 2 ) + 4 ln ( 3 ) ln ( 6 )}{2 ln ( 3 )}

十進法表記

x = 1, x = - 1.63092 \dots

解答ステップ

2^{x} \cdot 3^{x^{2}} = 6

指数の規則を適用する

(x + lo g_{2} (3) x^{2}) ln (2) = ln (6)

解く

(x + lo g_{2} (3) x^{2}) ln (2) = ln (6) : x = \frac{- ln ( 2 ) + ln ^{2} ( 2 ) + 4 ln ( 3 ) ln ( 6 )}{2 ln ( 3 )}, x = \frac{- ln ( 2 ) - ln ^{2} ( 2 ) + 4 ln ( 3 ) ln ( 6 )}{2 ln ( 3 )}

x = \frac{- ln ( 2 ) + ln ^{2} ( 2 ) + 4 ln ( 3 ) ln ( 6 )}{2 ln ( 3 )}, x = \frac{- ln ( 2 ) - ln ^{2} ( 2 ) + 4 ln ( 3 ) ln ( 6 )}{2 ln ( 3 )}