簡約 1/4 ln(10)+ln(13/4)-ln(9/2)

解

簡約

\frac{1}{4} ln (10) + ln (\frac{13}{4}) - ln (\frac{9}{2})

ln (\frac{13 4 10}{18})

十進法表記

0.25022 \dots

解答ステップ

\frac{1}{4} ln (10) + ln (\frac{13}{4}) - ln (\frac{9}{2})

対数の規則を適用する:

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

\frac{1}{4} ln (10) = ln (1 0^{\frac{1}{4}})

= ln (1 0^{\frac{1}{4}}) + ln (\frac{13}{4}) - ln (\frac{9}{2})

対数の規則を適用する:

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

ln (1 0^{\frac{1}{4}}) + ln (\frac{13}{4}) = ln (1 0^{\frac{1}{4}} \cdot \frac{13}{4})

= ln (1 0^{\frac{1}{4}} \cdot \frac{13}{4}) - ln (\frac{9}{2})

1 0^{\frac{1}{4}} \cdot \frac{13}{4} = \frac{13 4 10}{4}

= ln (\frac{13 4 10}{4}) - ln (\frac{9}{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{13 4 10}{4}) - ln (\frac{9}{2}) = ln (\frac{\frac{13 4 10}{4}}{\frac{9}{2}})

= ln (\frac{\frac{13 4 10}{4}}{\frac{9}{2}})

\frac{\frac{13 4 10}{4}}{\frac{9}{2}} = \frac{13 4 10}{18}

= ln (\frac{13 4 10}{18})