56^{x+7}=89^{x-10}

解

5 \cdot 6^{x + 7} = 8 \cdot 9^{x - 10}

x = \frac{20 ln ( 3 ) + 7 ln ( 6 ) + ln ( 5 ) - 3 ln ( 2 )}{ln ( \frac{3}{2} )}

十進法表記

x = 83.96421 \dots

解答ステップ

5 \cdot 6^{x + 7} = 8 \cdot 9^{x - 10}

指数の規則を適用する

ln (5) + (x + 7) ln (6) = ln (8) + (x - 10) ln (9)

解く

ln (5) + (x + 7) ln (6) = ln (8) + (x - 10) ln (9) : x = \frac{20 ln ( 3 ) + 7 ln ( 6 ) + ln ( 5 ) - 3 ln ( 2 )}{ln ( \frac{3}{2} )}

x = \frac{20 ln ( 3 ) + 7 ln ( 6 ) + ln ( 5 ) - 3 ln ( 2 )}{ln ( \frac{3}{2} )}