簡約 1/2 ln(25/22)

解

簡約

\frac{1}{2} ln (\frac{25}{22})

ln (5) - \frac{1}{2} ln (22)

十進法表記

0.06391 \dots

解答ステップ

\frac{1}{2} ln (\frac{25}{22})

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{25}{22}) = ln (25) - ln (22)

= \frac{1}{2} (ln (25) - ln (22))

ln (25) = 2 ln (5)

= \frac{1}{2} (2 ln (5) - ln (22))

分配法則を適用する:

a (b - c) = ab - a c

a = \frac{1}{2}, b = 2 ln (5), c = ln (22)

= \frac{1}{2} \cdot 2 ln (5) - \frac{1}{2} ln (22)

= 2 \cdot \frac{1}{2} ln (5) - \frac{1}{2} ln (22)

2 \cdot \frac{1}{2} ln (5) = ln (5)

= ln (5) - \frac{1}{2} ln (22)