簡約 ln(1)-ln((sqrt(3))/2)

解

簡約

ln (1) - ln (\frac{3}{2})

- (\frac{1}{2} ln (3) - ln (2))

十進法表記

0.14384 \dots

解答ステップ

ln (1) - ln (\frac{3}{2})

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{3}{2}) = ln (3) - ln (2)

= ln (1) - (ln (3) - ln (2))

対数の規則を適用する:

lo g_{a} (1) = 0

= 0 - (ln (3) - ln (2))

ln (3) = \frac{1}{2} ln (3)

= 0 - (\frac{1}{2} ln (3) - ln (2))

0 - (\frac{1}{2} ln (3) - ln (2)) = - (\frac{1}{2} ln (3) - ln (2))

= - (\frac{1}{2} ln (3) - ln (2))