簡約 ln(7)-(2/3)*ln(2)+ln(3)

解

簡約

ln (7) - (\frac{2}{3}) \cdot ln (2) + ln (3)

ln (\frac{21 3 2}{2})

十進法表記

2.58242 \dots

解答ステップ

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

対数の規則を適用する:

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

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

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

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

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

\frac{7}{2 ^{(\frac{2}{3})}} = \frac{7 3 2}{2}

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

対数の規則を適用する:

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

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

= ln (3 \cdot \frac{7 3 2}{2})

\frac{7 3 2}{2} \cdot 3 = \frac{21 3 2}{2}

= ln (\frac{21 3 2}{2})