簡約 4log_{10}(3x^2)-1/2 log_{10}(9x^8)

解

簡約

4 lo g_{10} (3 x^{2}) - \frac{1}{2} lo g_{10} (9 x^{8})

lo g_{10} (27 x^{4})

解答ステップ

4 lo g_{10} (3 x^{2}) - \frac{1}{2} lo g_{10} (9 x^{8})

4 lo g_{10} (3 x^{2}) = lo g_{10} ((3 x^{2})^{4})

- \frac{1}{2} lo g_{10} (9 x^{8}) = - lo g_{10} ((9 x^{8})^{\frac{1}{2}})

= lo g_{10} ((3 x^{2})^{4}) - lo g_{10} ((9 x^{8})^{\frac{1}{2}})

対数の規則を適用する:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} ((3 x^{2})^{4}) - lo g_{10} ((9 x^{8})^{\frac{1}{2}}) = lo g_{10} (\frac{( 3 x ^{2} ) ^{4}}{( 9 x ^{8} ) ^{\frac{1}{2}}})

= lo g_{10} (\frac{( 3 x ^{2} ) ^{4}}{( 9 x ^{8} ) ^{\frac{1}{2}}})

キャンセル

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

= lo g_{10} (27 x^{4})