展開する ln((y^3x^6)/((\sqrt[3]{z^2))w^4})

解

展開する

ln \frac{y ^{3} x ^{6}}{( 3 z ^{2} ) w ^{4}}

3 ln (y) + 6 ln (x) - ln (3 z^{2}) - 4 ln (w)

解答ステップ

ln \frac{y ^{3} x ^{6}}{( 3 z ^{2} ) w ^{4}}

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{y ^{3} x ^{6}}{( 3 z ^{2} ) w ^{4}} = ln (y^{3} x^{6}) - ln ((3 z^{2}) w^{4})

= ln (y^{3} x^{6}) - ln (w^{4} 3 z^{2})

対数の規則を適用する:

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

ln (y^{3} x^{6}) = ln (y^{3}) + ln (x^{6}), ln (3 z^{2} w^{4}) = ln (3 z^{2}) + ln (w^{4})

= ln (y^{3}) + ln (x^{6}) - (ln (3 z^{2}) + ln (w^{4}))

対数の規則を適用する:

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

ln (y^{3}) = 3 ln (y)

= 3 ln (y) + ln (x^{6}) - (ln (3 z^{2}) + ln (w^{4}))

対数の規則を適用する:

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

ln (x^{6}) = 6 ln (x)

= 3 ln (y) + 6 ln (x) - (ln (3 z^{2}) + ln (w^{4}))

対数の規則を適用する:

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

ln (w^{4}) = 4 ln (w)

= 3 ln (y) + 6 ln (x) - (ln (3 z^{2}) + 4 ln (w))

- (ln (3 z^{2}) + 4 ln (w)) : - ln (3 z^{2}) - 4 ln (w)

= 3 ln (y) + 6 ln (x) - ln (3 z^{2}) - 4 ln (w)