簡約 2log_{a}(4x^2)-1/6 log_{a}(2x+3)

解

簡約

2 lo g_{a} (4 x^{2}) - \frac{1}{6} lo g_{a} (2 x + 3)

lo g_{a} (\frac{16 x ^{4} ( 2 x + 3 ) ^{\frac{5}{6}}}{2 x + 3})

解答ステップ

2 lo g_{a} (4 x^{2}) - \frac{1}{6} lo g_{a} (2 x + 3)

対数の規則を適用する:

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

2 lo g_{a} (4 x^{2}) = lo g_{a} ((4 x^{2})^{2})

= lo g_{a} ((4 x^{2})^{2}) - \frac{1}{6} lo g_{a} (2 x + 3)

対数の規則を適用する:

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

\frac{1}{6} lo g_{a} (2 x + 3) = lo g_{a} ((2 x + 3)^{\frac{1}{6}})

= lo g_{a} ((4 x^{2})^{2}) - lo g_{a} ((2 x + 3)^{\frac{1}{6}})

対数の規則を適用する:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{a} ((4 x^{2})^{2}) - lo g_{a} ((2 x + 3)^{\frac{1}{6}}) = lo g_{a} (\frac{( 4 x ^{2} ) ^{2}}{( 2 x + 3 ) ^{\frac{1}{6}}})

= lo g_{a} (\frac{( 4 x ^{2} ) ^{2}}{( 2 x + 3 ) ^{\frac{1}{6}}})

簡素化

\frac{( 4 x ^{2} ) ^{2}}{( 2 x + 3 ) ^{\frac{1}{6}}} : \frac{16 x ^{4} ( 2 x + 3 ) ^{\frac{5}{6}}}{2 x + 3}

= lo g_{a} (\frac{16 x ^{4} ( 2 x + 3 ) ^{\frac{5}{6}}}{2 x + 3})