2^{5x+1}=81^{x-2}

解

2^{5 x + 1} = 8 1^{x - 2}

x = \frac{8 ln ( 3 ) + ln ( 2 )}{4 ln ( 3 ) - 5 ln ( 2 )}

十進法表記

x = 10.20987 \dots

解答ステップ

2^{5 x + 1} = 8 1^{x - 2}

指数の規則を適用する

(5 x + 1) ln (2) = (x - 2) ln (81)

解く

(5 x + 1) ln (2) = (x - 2) ln (81) : x = \frac{8 ln ( 3 ) + ln ( 2 )}{4 ln ( 3 ) - 5 ln ( 2 )}

x = \frac{8 ln ( 3 ) + ln ( 2 )}{4 ln ( 3 ) - 5 ln ( 2 )}