簡約 ln(233955/388533)-ln(1-233955/388533)

解

簡約

ln (\frac{233955}{388533}) - ln (1 - \frac{233955}{388533})

ln (\frac{77985}{51526})

十進法表記

0.41442 \dots

解答ステップ

ln (\frac{233955}{388533}) - ln (1 - \frac{233955}{388533})

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{233955}{388533}) - ln (1 - \frac{233955}{388533}) = ln (\frac{\frac{233955}{388533}}{- \frac{233955}{388533} + 1})

= ln (\frac{\frac{233955}{388533}}{1 - \frac{233955}{388533}})

\frac{\frac{233955}{388533}}{1 - \frac{233955}{388533}} = \frac{77985}{51526}

= ln (\frac{77985}{51526})