簡約 log_{10}(a) 1/4-log_{10}(b) 1/2

解

簡約

lo g_{10} (a) \frac{1}{4} - lo g_{10} (b) \frac{1}{2}

lo g_{10} (\frac{a ^{\frac{1}{4}} b}{b})

解答ステップ

lo g_{10} (a) \frac{1}{4} - lo g_{10} (b) \frac{1}{2}

対数の規則を適用する:

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

\frac{1}{4} lo g_{10} (a) = lo g_{10} (a^{\frac{1}{4}})

= lo g_{10} (a^{\frac{1}{4}}) - \frac{1}{2} lo g_{10} (b)

対数の規則を適用する:

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

\frac{1}{2} lo g_{10} (b) = lo g_{10} (b^{\frac{1}{2}})

= lo g_{10} (a^{\frac{1}{4}}) - lo g_{10} (b^{\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})

lo g_{10} (a^{\frac{1}{4}}) - lo g_{10} (b^{\frac{1}{2}}) = lo g_{10} (\frac{a ^{\frac{1}{4}}}{b ^{\frac{1}{2}}})

= lo g_{10} (\frac{a ^{\frac{1}{4}}}{b ^{\frac{1}{2}}})

簡素化

\frac{a ^{\frac{1}{4}}}{b ^{\frac{1}{2}}} : \frac{a ^{\frac{1}{4}} b}{b}

= lo g_{10} (\frac{a ^{\frac{1}{4}} b}{b})