簡約 (8.314298.15)/(296485)ln(1*10^{-7})

解

簡約

\frac{8.314 \cdot 298.15}{2 \cdot 96485} ln (1 \cdot 1 0^{- 7})

\frac{2478.8191}{192970} - 7 ln (10)

十進法表記

- 16.10525 \dots

解答ステップ

\frac{8.314 \cdot 298.15}{2 \cdot 96485} ln (1 \cdot 1 0^{- 7})

対数の規則を適用する:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

\frac{8.314 \cdot 298.15}{2 \cdot 96485} ln (1 \cdot 1 0^{- 7}) = \frac{8.314 \cdot 298.15}{2 \cdot 96485} ln (1) + \frac{8.314 \cdot 298.15}{2 \cdot 96485} ln (1 0^{- 7})

= \frac{8.314 \cdot 298.15}{2 \cdot 96485} ln (1) + \frac{8.314 \cdot 298.15}{2 \cdot 96485} ln (1 0^{- 7})

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (1 0^{- 7}) = - 7 ln (10)

= \frac{8.314 \cdot 298.15}{2 \cdot 96485} ln (1) + \frac{8.314 \cdot 298.15}{2 \cdot 96485} - 7 ln (10)

\frac{8.314 \cdot 298.15}{2 \cdot 96485} ln (1) = 0

\frac{8.314 \cdot 298.15}{2 \cdot 96485} = \frac{2478.8191}{192970}

= 0 + \frac{2478.8191}{192970} - 7 ln (10)

0 + \frac{2478.8191}{192970} - 7 ln (10) = \frac{2478.8191}{192970} - 7 ln (10)

= \frac{2478.8191}{192970} - 7 ln (10)