簡約 ln(12)+1/2 ln(x/2)+1/2 ln(x/2)

解

簡約

ln (12) + \frac{1}{2} ln (\frac{x}{2}) + \frac{1}{2} ln (\frac{x}{2})

ln (6 x)

解答ステップ

ln (12) + \frac{1}{2} ln (\frac{x}{2}) + \frac{1}{2} ln (\frac{x}{2})

対数の規則を適用する:

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

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

= ln (12) + ln ((\frac{x}{2})^{\frac{1}{2}}) + \frac{1}{2} ln (\frac{x}{2})

対数の規則を適用する:

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

ln (12) + ln ((\frac{x}{2})^{\frac{1}{2}}) = ln (12 (\frac{x}{2})^{\frac{1}{2}})

= ln (12 (\frac{x}{2})^{\frac{1}{2}}) + \frac{1}{2} ln (\frac{x}{2})

簡素化

12 (\frac{x}{2})^{\frac{1}{2}} : 62 x

= ln (62 x) + \frac{1}{2} ln (\frac{x}{2})

対数の規則を適用する:

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

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

= ln (62 x) + ln ((\frac{x}{2})^{\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 (62 x) + ln ((\frac{x}{2})^{\frac{1}{2}}) = ln (62 (\frac{x}{2})^{\frac{1}{2}} x)

= ln (62 (\frac{x}{2})^{\frac{1}{2}} x)

簡素化

62 x (\frac{x}{2})^{\frac{1}{2}} : 6 x

= ln (6 x)