簡約 5ln(2)-2ln(7/2)

解

簡約

5 ln (2) - 2 ln (\frac{7}{2})

ln (\frac{128}{49})

十進法表記

0.96020 \dots

解答ステップ

5 ln (2) - 2 ln (\frac{7}{2})

対数の規則を適用する:

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

5 ln (2) = ln (2^{5})

= ln (2^{5}) - 2 ln (\frac{7}{2})

対数の規則を適用する:

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

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

= ln (2^{5}) - ln ((\frac{7}{2})^{2})

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^{5}) - ln ((\frac{7}{2})^{2}) = ln (\frac{2 ^{5}}{( \frac{7}{2} ) ^{2}})

= ln (\frac{2 ^{5}}{( \frac{7}{2} ) ^{2}})

\frac{2 ^{5}}{( \frac{7}{2} ) ^{2}} = \frac{128}{49}

= ln (\frac{128}{49})