簡約 ln((4m^5)/p)

解

簡約

ln (\frac{4 m ^{5}}{p})

2 ln (2) + 5 ln (m) - ln (p)

解答ステップ

ln (\frac{4 m ^{5}}{p})

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{4 m ^{5}}{p}) = ln (4 m^{5}) - ln (p)

= ln (4 m^{5}) - ln (p)

対数の規則を適用する:

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

ln (4 m^{5}) = ln (4) + ln (m^{5})

= ln (4) + ln (m^{5}) - ln (p)

対数の規則を適用する:

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

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

= ln (4) + 5 ln (m) - ln (p)

ln (4) = 2 ln (2)

= 2 ln (2) + 5 ln (m) - ln (p)