簡約 e^{(5/4 (ln(x)-ln(5x-4))+c)}

解

簡約

e^{(\frac{5}{4} (l n (x) - l n (5 x - 4)) + c)}

e^{c} (\frac{x}{5 x - 4})^{\frac{5}{4}}

解答ステップ

e^{(\frac{5}{4} (l n (x) - l n (5 x - 4)) + c)}

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 (x) - ln (5 x - 4) = ln (\frac{x}{5 x - 4})

= e^{\frac{5}{4} l n (\frac{x}{5 x - 4}) + c}

指数の規則を適用する:

a^{b + c} = a^{b} a^{c}

= e^{\frac{5}{4} l n (\frac{x}{5 x - 4})} e^{c}

簡素化

e^{\frac{5}{4} l n (\frac{x}{5 x - 4})} : (\frac{x}{5 x - 4})^{\frac{5}{4}}

= (\frac{x}{5 x - 4})^{\frac{5}{4}} e^{c}

= e^{c} (\frac{x}{5 x - 4})^{\frac{5}{4}}