簡約 1/3 (ln(x)+ln(x-6)-ln(x^3+9))

解

簡約

\frac{1}{3} (ln (x) + ln (x - 6) - ln (x^{3} + 9))

\frac{1}{3} ln (\frac{x ( x - 6 )}{x ^{3} + 9})

解答ステップ

\frac{1}{3} (ln (x) + ln (x - 6) - ln (x^{3} + 9))

対数の規則を適用する:

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

ln (x) + ln (x - 6) = ln (x (x - 6))

= \frac{1}{3} (ln (x (x - 6)) - ln (x^{3} + 9))

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 - 6)) - ln (x^{3} + 9) = ln (\frac{x ( x - 6 )}{x ^{3} + 9})

= \frac{1}{3} ln (\frac{x ( x - 6 )}{x ^{3} + 9})