簡約 ln((tan^2(x))/(e^{4x^2)|x^5|})

解

簡約

ln (\frac{tan ^{2} ( x )}{e ^{4 x^{2}} ∣ x ^{5} ∣})

ln (tan^{2} (x)) - 4 x^{2} - ln x^{5}

解答ステップ

ln (\frac{tan ^{2} ( x )}{e ^{4 x^{2}} ∣ x ^{5} ∣})

対数の規則を適用する:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{tan ^{2} ( x )}{e ^{4 x^{2}} ∣ x ^{5} ∣}) = ln (tan^{2} (x)) - ln (e^{4 x^{2}} x^{5})

= ln (tan^{2} (x)) - ln (e^{4 x^{2}} x^{5})

対数の規則を適用する:

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

ln (e^{4 x^{2}} x^{5}) = ln (e^{4 x^{2}}) + ln x^{5}

= ln (tan^{2} (x)) - (ln (e^{4 x^{2}}) + ln x^{5})

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= ln (tan^{2} (x)) - (4 x^{2} ln (e) + ln x^{5})

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

= ln (tan^{2} (x)) - (4 x^{2} + ln x^{5})

- (4 x^{2} + ln x^{5}) : - 4 x^{2} - ln x^{5}

= ln (tan^{2} (x)) - 4 x^{2} - ln x^{5}