簡約 2(ln(5/2)-ln(3/2))

解

簡約

2 (ln (\frac{5}{2}) - ln (\frac{3}{2}))

2 ln (\frac{5}{3})

十進法表記

1.02165 \dots

解答ステップ

2 (ln (\frac{5}{2}) - ln (\frac{3}{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}{2}) - ln (\frac{3}{2}) = ln (\frac{\frac{5}{2}}{\frac{3}{2}})

= 2 ln (\frac{\frac{5}{2}}{\frac{3}{2}})

\frac{\frac{5}{2}}{\frac{3}{2}} = \frac{5}{3}

= 2 ln (\frac{5}{3})