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

解

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

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

十進法表記

x = - 2.14072 \dots

解答ステップ

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

指数の規則を適用する

(2 x + 1) ln (4) = (x - 2) ln (3)

解く

(2 x + 1) ln (4) = (x - 2) ln (3) : x = - \frac{2 ln ( 6 )}{4 ln ( 2 ) - ln ( 3 )}

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