簡約 (19.16)/(0.0004600.02)ln(1/(1-0.9))

解

簡約

\frac{19.16}{0.0004 \cdot 60 \cdot 0.02} ln (\frac{1}{1 - 0.9})

- \frac{19.16 ln ( 0.1 )}{0.00048}

十進法表記

91911.52162 \dots

解答ステップ

\frac{19.16}{0.0004 \cdot 60 \cdot 0.02} ln (\frac{1}{1 - 0.9})

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 - 0.9}) = ln (1) - ln (1 - 0.9)

= \frac{19.16}{60 \cdot 0.0004 \cdot 0.02} (ln (1) - ln (1 - 0.9))

分数を乗じる:

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

= \frac{19.16 ( ln ( 1 ) - ln ( 1 - 0.9 ) )}{0.0004 \cdot 60 \cdot 0.02}

数を引く:

1 - 0.9 = 0.1

= \frac{19.16 ( ln ( 1 ) - ln ( 0.1 ) )}{60 \cdot 0.0004 \cdot 0.02}

数を乗じる:

0.0004 \cdot 60 \cdot 0.02 = 0.00048

= \frac{19.16 ( ln ( 1 ) - ln ( 0.1 ) )}{0.00048}

対数の規則を適用する:

lo g_{a} (1) = 0

= \frac{19.16 ( - ln ( 0.1 ) + 0 )}{0.00048}

19.16 (0 - ln (0.1)) = - 19.16 ln (0.1)

= \frac{- 19.16 ln ( 0.1 )}{0.00048}

分数の規則を適用する:

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

= - \frac{19.16 ln ( 0.1 )}{0.00048}