簡約 2(log_{6}(y)-2log_{6}(w))+2log_{6}(x)

解

簡約

2 (lo g_{6} (y) - 2 lo g_{6} (w)) + 2 lo g_{6} (x)

lo g_{6} (\frac{y ^{2} x ^{2}}{w ^{4}})

解答ステップ

2 (lo g_{6} (y) - 2 lo g_{6} (w)) + 2 lo g_{6} (x)

対数の規則を適用する:

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

2 lo g_{6} (w) = lo g_{6} (w^{2})

= 2 (lo g_{6} (y) - lo g_{6} (w^{2})) + 2 lo g_{6} (x)

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_{6} (y) - lo g_{6} (w^{2}) = lo g_{6} (\frac{y}{w ^{2}})

= 2 lo g_{6} (\frac{y}{w ^{2}}) + 2 lo g_{6} (x)

対数の規則を適用する:

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

2 lo g_{6} (\frac{y}{w ^{2}}) = lo g_{6} ((\frac{y}{w ^{2}})^{2})

= lo g_{6} ((\frac{y}{w ^{2}})^{2}) + 2 lo g_{6} (x)

対数の規則を適用する:

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

2 lo g_{6} (x) = lo g_{6} (x^{2})

= lo g_{6} ((\frac{y}{w ^{2}})^{2}) + lo g_{6} (x^{2})

対数の規則を適用する:

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

lo g_{6} ((\frac{y}{w ^{2}})^{2}) + lo g_{6} (x^{2}) = lo g_{6} ((\frac{y}{w ^{2}})^{2} x^{2})

= lo g_{6} ((\frac{y}{w ^{2}})^{2} x^{2})

簡素化

(\frac{y}{w ^{2}})^{2} x^{2} : \frac{y ^{2} x ^{2}}{w ^{4}}

= lo g_{6} (\frac{y ^{2} x ^{2}}{w ^{4}})