簡約 1/2 ln(a)+1/2 ln(b)

解

簡約

\frac{1}{2} ln (a) + \frac{1}{2} ln (b)

ln (a^{\frac{1}{2}} b^{\frac{1}{2}})

解答ステップ

\frac{1}{2} ln (a) + \frac{1}{2} ln (b)

対数の規則を適用する:

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

\frac{1}{2} ln (a) = ln (a^{\frac{1}{2}})

= ln (a^{\frac{1}{2}}) + \frac{1}{2} ln (b)

対数の規則を適用する:

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

\frac{1}{2} ln (b) = ln (b^{\frac{1}{2}})

= ln (a^{\frac{1}{2}}) + ln (b^{\frac{1}{2}})

対数の規則を適用する:

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

ln (a^{\frac{1}{2}}) + ln (b^{\frac{1}{2}}) = ln (a^{\frac{1}{2}} b^{\frac{1}{2}})

= ln (a^{\frac{1}{2}} b^{\frac{1}{2}})