簡約 ln((e^4p^7)/(5n^2\sqrt[3]{m-1)})

解

簡約

ln (\frac{e ^{4} p ^{7}}{5 n ^{2} 3 m - 1})

4 + 7 ln (p) - ln (5) - 2 ln (n) - ln (3 m - 1)

解答ステップ

ln (\frac{e ^{4} p ^{7}}{5 n ^{2} 3 m - 1})

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{e ^{4} p ^{7}}{5 n ^{2} 3 m - 1}) = ln (e^{4} p^{7}) - ln (5 n^{2} 3 m - 1)

= ln (e^{4} p^{7}) - ln (5 n^{2} 3 m - 1)

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} p^{7}) = ln (e^{4}) + ln (p^{7}), ln (5 n^{2} 3 m - 1) = ln (5) + ln (n^{2}) + ln (3 m - 1)

= ln (e^{4}) + ln (p^{7}) - (ln (n^{2}) + ln (3 m - 1) + ln (5))

対数の規則を適用する:

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

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

= 4 ln (e) + ln (p^{7}) - (ln (5) + ln (n^{2}) + ln (3 m - 1))

対数の規則を適用する:

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

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

= 4 ln (e) + 7 ln (p) - (ln (5) + ln (n^{2}) + ln (3 m - 1))

対数の規則を適用する:

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

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

= 4 ln (e) + 7 ln (p) - (ln (5) + 2 ln (n) + ln (3 m - 1))

4 ln (e) = 4

= 4 + 7 ln (p) - (2 ln (n) + ln (3 m - 1) + ln (5))

- (ln (5) + 2 ln (n) + ln (3 m - 1)) : - ln (5) - 2 ln (n) - ln (3 m - 1)

= 4 + 7 ln (p) - ln (5) - 2 ln (n) - ln (3 m - 1)