5^{2x+1}=7^{x-3}

解

5^{2 x + 1} = 7^{x - 3}

x = - \frac{ln ( 1715 )}{2 ln ( 5 ) - ln ( 7 )}

十進法表記

x = - 5.85025 \dots

解答ステップ

5^{2 x + 1} = 7^{x - 3}

指数の規則を適用する

(2 x + 1) ln (5) = (x - 3) ln (7)

解く

(2 x + 1) ln (5) = (x - 3) ln (7) : x = - \frac{ln ( 1715 )}{2 ln ( 5 ) - ln ( 7 )}

x = - \frac{ln ( 1715 )}{2 ln ( 5 ) - ln ( 7 )}