3^{2(x-1)}=2^{x-3}

解

3^{2 (x - 1)} = 2^{x - 3}

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

十進法表記

x = 0.07830 \dots

解答ステップ

3^{2 (x - 1)} = 2^{x - 3}

指数の規則を適用する

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

解く

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

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