簡約 1/2 (ln(3)-3ln(2)+3ln(1))

解

簡約

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

\frac{1}{2} ln (\frac{3}{8})

十進法表記

- 0.49041 \dots

解答ステップ

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

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

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

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

2^{3} = 8

= \frac{1}{2} (ln (\frac{3}{8}) + 3 ln (1))

3 ln (1) = 0

= \frac{1}{2} (ln (\frac{3}{8}) + 0)

ln (\frac{3}{8}) + 0 = ln (\frac{3}{8})

= \frac{1}{2} ln (\frac{3}{8})