簡約 19/13+4/5 ln(5/4)+3/8 ln(2)

解

簡約

\frac{19}{13} + \frac{4}{5} ln (\frac{5}{4}) + \frac{3}{8} ln (2)

\frac{19}{13} + ln ((\frac{5}{4})^{\frac{4}{5}} \cdot 2^{\frac{3}{8}})

十進法表記

1.89998 \dots

解答ステップ

\frac{19}{13} + \frac{4}{5} ln (\frac{5}{4}) + \frac{3}{8} ln (2)

対数の規則を適用する:

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

\frac{4}{5} ln (\frac{5}{4}) = ln ((\frac{5}{4})^{\frac{4}{5}})

= \frac{19}{13} + ln ((\frac{5}{4})^{\frac{4}{5}}) + \frac{3}{8} ln (2)

対数の規則を適用する:

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

\frac{3}{8} ln (2) = ln (2^{\frac{3}{8}})

= \frac{19}{13} + ln ((\frac{5}{4})^{\frac{4}{5}}) + ln (2^{\frac{3}{8}})

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}{4})^{\frac{4}{5}}) + ln (2^{\frac{3}{8}}) = ln (2^{\frac{3}{8}} (\frac{5}{4})^{\frac{4}{5}})

= \frac{19}{13} + ln ((\frac{5}{4})^{\frac{4}{5}} \cdot 2^{\frac{3}{8}})