簡約 4ln(w)-1/5 ln(p)

解

簡約

4 ln (w) - \frac{1}{5} ln (p)

ln (\frac{w ^{4} p ^{\frac{4}{5}}}{p})

解答ステップ

4 ln (w) - \frac{1}{5} ln (p)

対数の規則を適用する:

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

4 ln (w) = ln (w^{4})

= ln (w^{4}) - \frac{1}{5} ln (p)

対数の規則を適用する:

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

\frac{1}{5} ln (p) = ln (p^{\frac{1}{5}})

= ln (w^{4}) - ln (p^{\frac{1}{5}})

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 (w^{4}) - ln (p^{\frac{1}{5}}) = ln (\frac{w ^{4}}{p ^{\frac{1}{5}}})

= ln (\frac{w ^{4}}{p ^{\frac{1}{5}}})

簡素化

\frac{w ^{4}}{p ^{\frac{1}{5}}} : \frac{w ^{4} p ^{\frac{4}{5}}}{p}

= ln (\frac{w ^{4} p ^{\frac{4}{5}}}{p})