簡約 (140.89)/(600.58)*ln(1/(1-0.1))

解

簡約

\frac{14 \cdot 0.89}{60 \cdot 0.58} \cdot ln (\frac{1}{1 - 0.1})

- \frac{12.46 ln ( 0.9 )}{34.8}

十進法表記

0.03772 \dots

解答ステップ

\frac{14 \cdot 0.89}{60 \cdot 0.58} ln (\frac{1}{1 - 0.1})

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{1}{1 - 0.1}) = ln (1) - ln (1 - 0.1)

= \frac{14 \cdot 0.89}{60 \cdot 0.58} (ln (1) - ln (1 - 0.1))

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{14 \cdot 0.89 ( ln ( 1 ) - ln ( 1 - 0.1 ) )}{60 \cdot 0.58}

14 \cdot 0.89 (ln (1) - ln (1 - 0.1)) = 12.46 (ln (1) - ln (0.9))

= \frac{12.46 ( ln ( 1 ) - ln ( 0.9 ) )}{60 \cdot 0.58}

数を乗じる:

60 \cdot 0.58 = 34.8

= \frac{12.46 ( ln ( 1 ) - ln ( 0.9 ) )}{34.8}

対数の規則を適用する:

lo g_{a} (1) = 0

= \frac{12.46 ( - ln ( 0.9 ) + 0 )}{34.8}

12.46 (0 - ln (0.9)) = - 12.46 ln (0.9)

= \frac{- 12.46 ln ( 0.9 )}{34.8}

分数の規則を適用する:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{12.46 ln ( 0.9 )}{34.8}