簡約 57/40+5/4 ln(4/5)+3/8 ln(2)

解

簡約

\frac{57}{40} + \frac{5}{4} ln (\frac{4}{5}) + \frac{3}{8} ln (2)

\frac{57}{40} + ln ((\frac{4}{5})^{\frac{5}{4}} \cdot 2^{\frac{3}{8}})

十進法表記

1.40600 \dots

解答ステップ

\frac{57}{40} + \frac{5}{4} ln (\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{5}{4} ln (\frac{4}{5}) = ln ((\frac{4}{5})^{\frac{5}{4}})

= \frac{57}{40} + ln ((\frac{4}{5})^{\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{3}{8} ln (2) = ln (2^{\frac{3}{8}})

= \frac{57}{40} + ln ((\frac{4}{5})^{\frac{5}{4}}) + 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{4}{5})^{\frac{5}{4}}) + ln (2^{\frac{3}{8}}) = ln (2^{\frac{3}{8}} (\frac{4}{5})^{\frac{5}{4}})

= \frac{57}{40} + ln ((\frac{4}{5})^{\frac{5}{4}} \cdot 2^{\frac{3}{8}})