簡約 ln((p^6q^7)/(4\sqrt[6]{r)})

解

簡約

ln (\frac{p ^{6} q ^{7}}{4 6 r})

6 ln (p) + 7 ln (q) - 2 ln (2) - ln (6 r)

解答ステップ

ln (\frac{p ^{6} q ^{7}}{4 6 r})

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{p ^{6} q ^{7}}{4 6 r}) = ln (p^{6} q^{7}) - ln (4 6 r)

= ln (p^{6} q^{7}) - ln (4 6 r)

対数の規則を適用する:

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

ln (p^{6} q^{7}) = ln (p^{6}) + ln (q^{7}), ln (4 6 r) = ln (4) + ln (6 r)

= ln (p^{6}) + ln (q^{7}) - (ln (6 r) + ln (4))

対数の規則を適用する:

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

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

= 6 ln (p) + ln (q^{7}) - (ln (4) + ln (6 r))

対数の規則を適用する:

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

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

= 6 ln (p) + 7 ln (q) - (ln (4) + ln (6 r))

ln (4) = 2 ln (2)

= 6 ln (p) + 7 ln (q) - (ln (6 r) + 2 ln (2))

- (2 ln (2) + ln (6 r)) : - 2 ln (2) - ln (6 r)

= 6 ln (p) + 7 ln (q) - 2 ln (2) - ln (6 r)