展開する 1/2 ln(6)+1/2 ln(x)-1/2 ln(x-6)

解

展開する

\frac{1}{2} ln (6) + \frac{1}{2} ln (x) - \frac{1}{2} ln (x - 6)

ln (\frac{6 ^{\frac{1}{2}} x ^{\frac{1}{2}} x - 6}{x - 6})

解答ステップ

\frac{1}{2} ln (6) + \frac{1}{2} ln (x) - \frac{1}{2} ln (x - 6)

対数の規則を適用する:

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

\frac{1}{2} ln (6) = ln (6^{\frac{1}{2}})

= ln (6^{\frac{1}{2}}) + \frac{1}{2} ln (x) - \frac{1}{2} ln (x - 6)

対数の規則を適用する:

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

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

= ln (6^{\frac{1}{2}}) + ln (x^{\frac{1}{2}}) - \frac{1}{2} ln (x - 6)

対数の規則を適用する:

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

ln (6^{\frac{1}{2}}) + ln (x^{\frac{1}{2}}) = ln (6^{\frac{1}{2}} x^{\frac{1}{2}})

= ln (6^{\frac{1}{2}} x^{\frac{1}{2}}) - \frac{1}{2} ln (x - 6)

対数の規則を適用する:

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

\frac{1}{2} ln (x - 6) = ln ((x - 6)^{\frac{1}{2}})

= ln (6^{\frac{1}{2}} x^{\frac{1}{2}}) - ln ((x - 6)^{\frac{1}{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 (6^{\frac{1}{2}} x^{\frac{1}{2}}) - ln ((x - 6)^{\frac{1}{2}}) = ln (\frac{6 ^{\frac{1}{2}} x ^{\frac{1}{2}}}{( x - 6 ) ^{\frac{1}{2}}})

= ln (\frac{6 ^{\frac{1}{2}} x ^{\frac{1}{2}}}{( x - 6 ) ^{\frac{1}{2}}})

\frac{6 ^{\frac{1}{2}} x ^{\frac{1}{2}}}{( x - 6 ) ^{\frac{1}{2}}} = \frac{6 ^{\frac{1}{2}} x ^{\frac{1}{2}} x - 6}{x - 6}

= ln (\frac{6 ^{\frac{1}{2}} x ^{\frac{1}{2}} x - 6}{x - 6})