208(1.04)^t=279(1.01)^t

解

208 (1.04)^{t} = 279 (1.01)^{t}

t = \frac{ln ( 279 ) - ln ( 208 )}{ln ( 1.04 ) - ln ( 1.01 )}

十進法表記

t = 10.03313 \dots

解答ステップ

208 (1.04)^{t} = 279 (1.01)^{t}

指数の規則を適用する

ln (208) + t ln (1.04) = ln (279) + t ln (1.01)

解く

ln (208) + t ln (1.04) = ln (279) + t ln (1.01) : t = \frac{ln ( 279 ) - ln ( 208 )}{ln ( 1.04 ) - ln ( 1.01 )}

t = \frac{ln ( 279 ) - ln ( 208 )}{ln ( 1.04 ) - ln ( 1.01 )}