簡約 13/8*ln(13/8)-1/(13/8)

解

簡約

\frac{13}{8} \cdot ln (\frac{13}{8}) - \frac{1}{\frac{13}{8}}

\frac{13}{8} (ln (13) - 3 ln (2)) - \frac{8}{13}

十進法表記

0.17356 \dots

解答ステップ

\frac{13}{8} ln (\frac{13}{8}) - \frac{1}{\frac{13}{8}}

対数の規則を適用する:

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

ln (\frac{13}{8}) = ln (13) - ln (8)

= \frac{13}{8} (ln (13) - ln (8)) - \frac{1}{\frac{13}{8}}

ln (8) = 3 ln (2)

= \frac{13}{8} (ln (13) - 3 ln (2)) - \frac{1}{\frac{13}{8}}

分数の規則を適用する:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{13}{8} (ln (13) - 3 ln (2)) - \frac{8}{13}