簡約-ln(75)-3ln(15/22)

解

簡約

- ln (75) - 3 ln (\frac{15}{22})

- ln (\frac{253125}{10648})

十進法表記

- 3.16851 \dots

解答ステップ

- ln (75) - 3 ln (\frac{15}{22})

対数の規則を適用する:

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

3 ln (\frac{15}{22}) = ln ((\frac{15}{22})^{3})

= - ln (75) - ln ((\frac{15}{22})^{3})

- ln (75) - ln ((\frac{15}{22})^{3})

を書き換え

- (ln (75) + ln ((\frac{15}{22})^{3}))

= - (ln (75) + ln ((\frac{15}{22})^{3}))

対数の規則を適用する:

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

ln (75) + ln ((\frac{15}{22})^{3}) = ln (75 (\frac{15}{22})^{3})

= - ln (75 (\frac{15}{22})^{3})

75 (\frac{15}{22})^{3} = \frac{253125}{10648}

= - ln (\frac{253125}{10648})