簡約 1/2 ln(130/100)

解

簡約

\frac{1}{2} ln (\frac{130}{100})

\frac{1}{2} ln (130) - ln (10)

十進法表記

0.13118 \dots

解答ステップ

\frac{1}{2} ln (\frac{130}{100})

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{130}{100}) = ln (130) - ln (100)

= \frac{1}{2} (ln (130) - ln (100))

ln (100) = 2 ln (10)

= \frac{1}{2} (ln (130) - 2 ln (10))

分配法則を適用する:

a (b - c) = ab - a c

a = \frac{1}{2}, b = ln (130), c = 2 ln (10)

= \frac{1}{2} ln (130) - \frac{1}{2} \cdot 2 ln (10)

= \frac{1}{2} ln (130) - 2 \cdot \frac{1}{2} ln (10)

2 \cdot \frac{1}{2} ln (10) = ln (10)

= \frac{1}{2} ln (130) - ln (10)