簡約 4ln(x+6/4)+ln(x+1)

解

簡約

4 ln (x + \frac{6}{4}) + ln (x + 1)

ln ((x + \frac{3}{2})^{4} (x + 1))

解答ステップ

4 ln (x + \frac{6}{4}) + ln (x + 1)

対数の規則を適用する:

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

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

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

対数の規則を適用する:

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

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

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

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

= ln ((x + \frac{3}{2})^{4} (x + 1))