簡約 ln((((tan(x))^4))/(e^{4x^4)x^7})

解

簡約

ln \frac{( ( tan ( x ) ) ^{4} )}{e ^{4 x^{4}} x ^{7}}

4 ln (tan (x)) - 4 x^{4} - 7 ln (x)

解答ステップ

ln \frac{( ( tan ( x ) ) ^{4} )}{e ^{4 x^{4}} x ^{7}}

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 ^{4} ( x ) )}{e ^{4 x^{4}} x ^{7}}) = ln ((tan^{4} (x))) - ln (e^{4 x^{4}} x^{7})

= ln (tan^{4} (x)) - ln (e^{4 x^{4}} x^{7})

対数の規則を適用する:

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

ln (tan^{4} (x)) = 4 ln (tan (x))

= 4 ln (tan (x)) - ln (e^{4 x^{4}} x^{7})

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^{4}} x^{7}) = ln (e^{4 x^{4}}) + ln (x^{7})

= 4 ln (tan (x)) - (ln (e^{4 x^{4}}) + ln (x^{7}))

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

= 4 ln (tan (x)) - (4 x^{4} ln (e) + ln (x^{7}))

対数の規則を適用する:

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

ln (x^{7}) = 7 ln (x)

= 4 ln (tan (x)) - (4 x^{4} ln (e) + 7 ln (x))

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

= 4 ln (tan (x)) - (4 x^{4} + 7 ln (x))

- (4 x^{4} + 7 ln (x)) : - 4 x^{4} - 7 ln (x)

= 4 ln (tan (x)) - 4 x^{4} - 7 ln (x)