簡約 (ln(ln(1/(1-0.4))-9ln(250)))/(-9)

解

簡約

\frac{ln ( ln ( \frac{1}{1 - 0.4} ) - 9 ln ( 250 ) )}{- 9}

- \frac{ln ( ln ( 4.36907 E - 22 ) )}{9}

解答ステップ

\frac{ln ( ln ( \frac{1}{1 - 0.4} ) - 9 ln ( 250 ) )}{- 9}

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

9 ln (250) = ln (25 0^{9})

= \frac{ln ( ln ( \frac{1}{1 - 0.4} ) - ln ( 25 0 ^{9} ) )}{- 9}

対数の規則を適用する:

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

ln (\frac{1}{1 - 0.4}) - ln (25 0^{9}) = ln (\frac{\frac{1}{1 - 0.4}}{25 0 ^{9}})

= \frac{ln ( ln ( \frac{\frac{1}{1 - 0.4}}{25 0 ^{9}} ) )}{- 9}

\frac{\frac{1}{1 - 0.4}}{25 0 ^{9}} = 4.36907 E - 22

= \frac{ln ( ln ( 4.36907 E - 22 ) )}{- 9}

分数の規則を適用する:

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

= - \frac{ln ( ln ( 4.36907 E - 22 ) )}{9}