簡約 ln((w^5x^{4/5})/(y^8z^7))

解

簡約

ln (\frac{w ^{5} x ^{\frac{4}{5}}}{y ^{8} z ^{7}})

5 ln (w) + \frac{4}{5} ln (x) - 8 ln (y) - 7 ln (z)

解答ステップ

ln (\frac{w ^{5} x ^{\frac{4}{5}}}{y ^{8} z ^{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{w ^{5} x ^{\frac{4}{5}}}{y ^{8} z ^{7}}) = ln (w^{5} x^{\frac{4}{5}}) - ln (y^{8} z^{7})

= ln (w^{5} x^{\frac{4}{5}}) - ln (y^{8} z^{7})

対数の規則を適用する:

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

ln (w^{5} x^{\frac{4}{5}}) = ln (w^{5}) + ln (x^{\frac{4}{5}}), ln (y^{8} z^{7}) = ln (y^{8}) + ln (z^{7})

= ln (w^{5}) + ln (x^{\frac{4}{5}}) - (ln (y^{8}) + ln (z^{7}))

対数の規則を適用する:

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

ln (w^{5}) = 5 ln (w)

= 5 ln (w) + ln (x^{\frac{4}{5}}) - (ln (y^{8}) + ln (z^{7}))

対数の規則を適用する:

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

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

= 5 ln (w) + \frac{4}{5} ln (x) - (ln (y^{8}) + ln (z^{7}))

対数の規則を適用する:

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

ln (y^{8}) = 8 ln (y)

= 5 ln (w) + \frac{4}{5} ln (x) - (8 ln (y) + ln (z^{7}))

対数の規則を適用する:

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

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

= 5 ln (w) + \frac{4}{5} ln (x) - (8 ln (y) + 7 ln (z))

- (8 ln (y) + 7 ln (z)) : - 8 ln (y) - 7 ln (z)

= 5 ln (w) + \frac{4}{5} ln (x) - 8 ln (y) - 7 ln (z)