3^{2x-3}=5^{3x-1}

解

3^{2 x - 3} = 5^{3 x - 1}

x = \frac{- ln ( 5 ) + 3 ln ( 3 )}{2 ln ( 3 ) - 3 ln ( 5 )}

十進法表記

x = - 0.64095 \dots

解答ステップ

3^{2 x - 3} = 5^{3 x - 1}

指数の規則を適用する

(2 x - 3) ln (3) = (3 x - 1) ln (5)

解く

(2 x - 3) ln (3) = (3 x - 1) ln (5) : x = \frac{- ln ( 5 ) + 3 ln ( 3 )}{2 ln ( 3 ) - 3 ln ( 5 )}

x = \frac{- ln ( 5 ) + 3 ln ( 3 )}{2 ln ( 3 ) - 3 ln ( 5 )}