化简 ln((\sqrt[5]{x^2yz})/(b^2w^{1/2)})

解答

化简

ln (\frac{5 x ^{2} yz}{b ^{2} w ^{\frac{1}{2}}})

ln (5 x^{2} yz) - 2 ln (b) - \frac{1}{2} ln (w)

求解步骤

ln (\frac{5 x ^{2} yz}{b ^{2} w ^{\frac{1}{2}}})

使用对数计算法则:

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

ln (\frac{5 x ^{2} yz}{b ^{2} w ^{\frac{1}{2}}}) = ln (5 x^{2} yz) - ln (b^{2} w^{\frac{1}{2}})

= ln (5 x^{2} yz) - ln (b^{2} w^{\frac{1}{2}})

使用对数计算法则:

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

ln (b^{2} w^{\frac{1}{2}}) = ln (b^{2}) + ln (w^{\frac{1}{2}})

= ln (5 x^{2} yz) - (ln (w^{\frac{1}{2}}) + ln (b^{2}))

使用对数计算法则:

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

ln (b^{2}) = 2 ln (b)

= ln (5 x^{2} yz) - (2 ln (b) + ln (w^{\frac{1}{2}}))

使用对数计算法则:

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

ln (w^{\frac{1}{2}}) = \frac{1}{2} ln (w)

= ln (5 x^{2} yz) - (2 ln (b) + \frac{1}{2} ln (w))

- (2 ln (b) + \frac{1}{2} ln (w)) : - 2 ln (b) - \frac{1}{2} ln (w)

= ln (5 x^{2} yz) - 2 ln (b) - \frac{1}{2} ln (w)

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