簡約 2.69-(0.02569)/2 ln((0.4^3)/(2^2))

解

簡約

2.69 - \frac{0.02569}{2} ln (\frac{0. 4 ^{3}}{2 ^{2}})

2.69 - \frac{0.07707}{2} ln (0.4) + 0.02569 ln (2)

十進法表記

2.74311 \dots

解答ステップ

2.69 - \frac{0.02569}{2} ln (\frac{0. 4 ^{3}}{2 ^{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{0. 4 ^{3}}{2 ^{2}}) = ln (0. 4^{3}) - ln (2^{2})

= 2.69 - \frac{0.02569}{2} (ln (0. 4^{3}) - ln (2^{2}))

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (0. 4^{3}) = 3 ln (0.4)

= 2.69 - \frac{0.02569}{2} (3 ln (0.4) - ln (2^{2}))

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 2.69 - \frac{0.02569}{2} (3 ln (0.4) - 2 ln (2))

拡張

- \frac{0.02569}{2} (3 ln (0.4) - 2 ln (2)) : - \frac{0.07707}{2} ln (0.4) + 0.02569 ln (2)

= 2.69 - \frac{0.07707}{2} ln (0.4) + 0.02569 ln (2)