簡約 4ln(3x^2)-1/2 ln(9x^8)

解

簡約

4 ln (3 x^{2}) - \frac{1}{2} ln (9 x^{8})

ln (27 x^{4})

解答ステップ

4 ln (3 x^{2}) - \frac{1}{2} ln (9 x^{8})

対数の規則を適用する:

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

4 ln (3 x^{2}) = ln ((3 x^{2})^{4})

= ln ((3 x^{2})^{4}) - \frac{1}{2} ln (9 x^{8})

対数の規則を適用する:

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

\frac{1}{2} ln (9 x^{8}) = ln ((9 x^{8})^{\frac{1}{2}})

= ln ((3 x^{2})^{4}) - ln ((9 x^{8})^{\frac{1}{2}})

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 ((3 x^{2})^{4}) - ln ((9 x^{8})^{\frac{1}{2}}) = ln (\frac{( 3 x ^{2} ) ^{4}}{( 9 x ^{8} ) ^{\frac{1}{2}}})

= ln (\frac{( 3 x ^{2} ) ^{4}}{( 9 x ^{8} ) ^{\frac{1}{2}}})

簡素化

\frac{( 3 x ^{2} ) ^{4}}{( 9 x ^{8} ) ^{\frac{1}{2}}} : 27 x^{4}

= ln (27 x^{4})