簡約 (1/2)^3-24ln(1/2)+3

解

簡約

(\frac{1}{2})^{3} - 24 ln (\frac{1}{2}) + 3

24 ln (2) + \frac{25}{8}

十進法表記

19.76053 \dots

解答ステップ

(\frac{1}{2})^{3} - 24 ln (\frac{1}{2}) + 3

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{1}{2}) = ln (1) - ln (2)

= (\frac{1}{2})^{3} - 24 (ln (1) - ln (2)) + 3

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

24 (ln (1) - ln (2)) = - 24 ln (2)

= \frac{1}{2 ^{3}} - (- 24 ln (2)) + 3

規則を適用

- (- a) = a

= \frac{1}{2 ^{3}} + 24 ln (2) + 3

2^{3} = 8

= \frac{1}{8} + 24 ln (2) + 3

分数を組み合わせる

3 + \frac{1}{8} : \frac{25}{8}

= 24 ln (2) + \frac{25}{8}