簡約 0-(0.025693)/2 ln(3/(2.4*10^{-3)})

解

簡約

0 - \frac{0.025693}{2} ln (\frac{3}{2.4 \cdot 1 0 ^{- 3}})

- \frac{0.025693}{2} (ln (3) - ln (\frac{2.4}{1000}))

十進法表記

- 0.09160 \dots

解答ステップ

0 - \frac{0.025693}{2} ln (\frac{3}{2.4 \cdot 1 0 ^{- 3}})

対数の規則を適用する:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{3}{2.4 \cdot 1 0 ^{- 3}}) = ln (3) - ln (2.4 \cdot 1 0^{- 3})

= 0 - \frac{0.025693}{2} (ln (3) - ln (1 0^{- 3} \cdot 2.4))

ln (2.4 \cdot 1 0^{- 3}) = ln (\frac{2.4}{1000})

= 0 - \frac{0.025693}{2} (ln (3) - ln (\frac{2.4}{1000}))

0 - \frac{0.025693}{2} (ln (3) - ln (\frac{2.4}{1000})) = - \frac{0.025693}{2} (ln (3) - ln (\frac{2.4}{1000}))

= - \frac{0.025693}{2} (ln (3) - ln (\frac{2.4}{1000}))