簡約 9ln(6)-ln(2!)+7ln(2)-ln(7!)-3*6

解

簡約

9 \cdot ln (6) - ln (2!) + 7 \cdot ln (2) - ln (7!) - 3 \cdot 6

ln (5038848) + ln (\frac{8}{315}) - 18

十進法表記

- 6.24044 \dots

解答ステップ

9 ln (6) - ln (2!) + 7 ln (2) - ln (7!) - 3 \cdot 6

対数の規則を適用する:

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

9 ln (6) = ln (6^{9})

= ln (6^{9}) - ln (2!) + 7 ln (2) - ln (7!) - 3 \cdot 6

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 (6^{9}) - ln (2!) = ln (\frac{6 ^{9}}{2 !})

= ln (\frac{6 ^{9}}{2 !}) + 7 ln (2) - ln (7!) - 3 \cdot 6

\frac{6 ^{9}}{2 !} = 5038848

= ln (5038848) + 7 ln (2) - ln (7!) - 3 \cdot 6

対数の規則を適用する:

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

7 ln (2) = ln (2^{7})

= ln (5038848) + ln (2^{7}) - ln (7!) - 3 \cdot 6

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 (2^{7}) - ln (7!) = ln (\frac{2 ^{7}}{7 !})

= ln (5038848) + ln (\frac{2 ^{7}}{7 !}) - 3 \cdot 6

\frac{2 ^{7}}{7 !} = \frac{8}{315}

= ln (5038848) + ln (\frac{8}{315}) - 3 \cdot 6

数を乗じる:

3 \cdot 6 = 18

= ln (5038848) + ln (\frac{8}{315}) - 18