簡約 7*ln(-1/2 ln(81))

解

簡約

7 \cdot ln (- \frac{1}{2} ln (81))

- 7 ln (2) + 7 ln (4 ln (3))

十進法表記

5.51036 \dots

解答ステップ

7 ln (- \frac{1}{2} ln (81))

対数の規則を適用する:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

7 ln (- \frac{1}{2} ln (81)) = 7 ln (\frac{1}{2}) + 7 ln (ln (81))

= 7 ln (\frac{1}{2}) + 7 ln (ln (81))

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)

= 7 (ln (1) - ln (2)) + 7 ln (ln (81))

7 (ln (1) - ln (2)) = - 7 ln (2)

= - 7 ln (2) + 7 ln (ln (81))

簡素化

ln (81) : 4 ln (3)

= - 7 ln (2) + 7 ln (4 ln (3))