440*1.007^t=3383

解

440 \cdot 1.00 7^{t} = 3383

t = \frac{ln ( \frac{3383}{440} )}{ln ( 1.007 )}

十進法表記

t = 292.41060 \dots

解答ステップ

440 \cdot 1.00 7^{t} = 3383

以下で両辺を割る

440

1.00 7^{t} = \frac{3383}{440}

指数の規則を適用する

t ln (1.007) = ln (\frac{3383}{440})

解く

t ln (1.007) = ln (\frac{3383}{440}) : t = \frac{ln ( \frac{3383}{440} )}{ln ( 1.007 )}

t = \frac{ln ( \frac{3383}{440} )}{ln ( 1.007 )}