簡約 4(ln(3)-ln(2))+6(ln(7)-ln(6))

解

簡約

4 (ln (3) - ln (2)) + 6 (ln (7) - ln (6))

ln (\frac{117649}{9216})

十進法表記

2.54676 \dots

解答ステップ

4 (ln (3) - ln (2)) + 6 (ln (7) - ln (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 (3) - ln (2) = ln (\frac{3}{2})

= 4 ln (\frac{3}{2}) + 6 (ln (7) - ln (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 (7) - ln (6) = ln (\frac{7}{6})

= 4 ln (\frac{3}{2}) + 6 ln (\frac{7}{6})

対数の規則を適用する:

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

4 ln (\frac{3}{2}) = ln ((\frac{3}{2})^{4})

= ln ((\frac{3}{2})^{4}) + 6 ln (\frac{7}{6})

対数の規則を適用する:

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

6 ln (\frac{7}{6}) = ln ((\frac{7}{6})^{6})

= ln ((\frac{3}{2})^{4}) + ln ((\frac{7}{6})^{6})

対数の規則を適用する:

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

ln ((\frac{3}{2})^{4}) + ln ((\frac{7}{6})^{6}) = ln ((\frac{7}{6})^{6} (\frac{3}{2})^{4})

= ln ((\frac{7}{6})^{6} (\frac{3}{2})^{4})

(\frac{3}{2})^{4} (\frac{7}{6})^{6} = \frac{117649}{9216}

= ln (\frac{117649}{9216})