簡約-(ln(5/4)-ln(7)+ln(5))/2

解

簡約

- \frac{ln ( \frac{5}{4} ) - ln ( 7 ) + ln ( 5 )}{2}

- \frac{ln ( \frac{25}{28} )}{2}

十進法表記

0.05666 \dots

解答ステップ

- \frac{ln ( \frac{5}{4} ) - ln ( 7 ) + ln ( 5 )}{2}

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{5}{4}) - ln (7) = ln (\frac{\frac{5}{4}}{7})

= - \frac{ln ( 5 ) + ln ( \frac{\frac{5}{4}}{7} )}{2}

\frac{\frac{5}{4}}{7} = \frac{5}{28}

= - \frac{ln ( \frac{5}{28} ) + ln ( 5 )}{2}

対数の規則を適用する:

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

ln (\frac{5}{28}) + ln (5) = ln (5 \cdot \frac{5}{28})

= - \frac{ln ( 5 \cdot \frac{5}{28} )}{2}

\frac{5}{28} \cdot 5 = \frac{25}{28}

= - \frac{ln ( \frac{25}{28} )}{2}