簡約 1/3 ln((x-4)^6)+ln(x)-ln(x^2-8x+16)

解

簡約

\frac{1}{3} ln ((x - 4)^{6}) + ln (x) - ln (x^{2} - 8 x + 16)

ln (x)

解答ステップ

\frac{1}{3} ln ((x - 4)^{6}) + ln (x) - ln (x^{2} - 8 x + 16)

対数の規則を適用する:

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

\frac{1}{3} ln ((x - 4)^{6}) = ln (((x - 4)^{6})^{\frac{1}{3}})

= ln (((x - 4)^{6})^{\frac{1}{3}}) + ln (x) - ln (x^{2} - 8 x + 16)

対数の規則を適用する:

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

ln (((x - 4)^{6})^{\frac{1}{3}}) + ln (x) = ln (x ((x - 4)^{6})^{\frac{1}{3}})

= ln (x ((x - 4)^{6})^{\frac{1}{3}}) - ln (x^{2} - 8 x + 16)

((x - 4)^{6})^{\frac{1}{3}} = (x - 4)^{2}

= ln (x (x - 4)^{2}) - ln (x^{2} - 8 x + 16)

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 (x (x - 4)^{2}) - ln (x^{2} - 8 x + 16) = ln (\frac{x ( x - 4 ) ^{2}}{x ^{2} - 8 x + 16})

= ln (\frac{x ( x - 4 ) ^{2}}{x ^{2} - 8 x + 16})

簡素化

\frac{x ( x - 4 ) ^{2}}{x ^{2} - 8 x + 16} : x

= ln (x)