簡約-2/3 log_{b}(x+1)-log_{b}(x+2)

解

簡約

- \frac{2}{3} lo g_{b} (x + 1) - lo g_{b} (x + 2)

- lo g_{b} ((x + 1)^{\frac{2}{3}} (x + 2))

解答ステップ

- \frac{2}{3} lo g_{b} (x + 1) - lo g_{b} (x + 2)

対数の規則を適用する:

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

\frac{2}{3} lo g_{b} (x + 1) = lo g_{b} ((x + 1)^{\frac{2}{3}})

= - lo g_{b} ((x + 1)^{\frac{2}{3}}) - lo g_{b} (x + 2)

- lo g_{b} ((x + 1)^{\frac{2}{3}}) - lo g_{b} (x + 2)

を書き換え

- (lo g_{b} ((x + 1)^{\frac{2}{3}}) + lo g_{b} (x + 2))

= - (lo g_{b} (x + 2) + lo g_{b} ((x + 1)^{\frac{2}{3}}))

対数の規則を適用する:

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

lo g_{b} ((x + 1)^{\frac{2}{3}}) + lo g_{b} (x + 2) = lo g_{b} ((x + 2) (x + 1)^{\frac{2}{3}})

= - lo g_{b} ((x + 1)^{\frac{2}{3}} (x + 2))