2^{2x+6}=3^{x-9}

解

2^{2 x + 6} = 3^{x - 9}

x = \frac{- 9 ln ( 3 ) - 6 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

十進法表記

x = - 48.82610 \dots

解答ステップ

2^{2 x + 6} = 3^{x - 9}

指数の規則を適用する

(2 x + 6) ln (2) = (x - 9) ln (3)

解く

(2 x + 6) ln (2) = (x - 9) ln (3) : x = \frac{- 9 ln ( 3 ) - 6 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

x = \frac{- 9 ln ( 3 ) - 6 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}