2^{2x+18}=3^{x-12}

解

2^{2 x + 18} = 3^{x - 12}

x = \frac{- 12 ln ( 3 ) - 18 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

十進法表記

x = - 89.19567 \dots

解答ステップ

2^{2 x + 18} = 3^{x - 12}

指数の規則を適用する

(2 x + 18) ln (2) = (x - 12) ln (3)

解く

(2 x + 18) ln (2) = (x - 12) ln (3) : x = \frac{- 12 ln ( 3 ) - 18 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

x = \frac{- 12 ln ( 3 ) - 18 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}