3^{2x-8}=5^{2x-8}

解

3^{2 x - 8} = 5^{2 x - 8}

x = - \frac{8 ln ( 5 ) - 8 ln ( 3 )}{2 ( ln ( 3 ) - ln ( 5 ) )}

十進法表記

x = 4

解答ステップ

3^{2 x - 8} = 5^{2 x - 8}

指数の規則を適用する

(2 x - 8) ln (3) = (2 x - 8) ln (5)

解く

(2 x - 8) ln (3) = (2 x - 8) ln (5) : x = - \frac{8 ln ( 5 ) - 8 ln ( 3 )}{2 ( ln ( 3 ) - ln ( 5 ) )}

x = - \frac{8 ln ( 5 ) - 8 ln ( 3 )}{2 ( ln ( 3 ) - ln ( 5 ) )}