簡約-5ln(a/c)-1ln(c/a)

解

簡約

- 5 ln (\frac{a}{c}) - 1 ln (\frac{c}{a})

- ln (\frac{a ^{4}}{c ^{4}})

解答ステップ

- 5 ln (\frac{a}{c}) - 1 \cdot ln (\frac{c}{a})

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

5 ln (\frac{a}{c}) = ln ((\frac{a}{c})^{5})

= - ln ((\frac{a}{c})^{5}) - 1 \cdot ln (\frac{c}{a})

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

1 \cdot ln (\frac{c}{a}) = ln ((\frac{c}{a})^{1})

= - ln ((\frac{a}{c})^{5}) - ln ((\frac{c}{a})^{1})

- ln ((\frac{a}{c})^{5}) - ln ((\frac{c}{a})^{1})

を書き換え

- (ln ((\frac{a}{c})^{5}) + ln ((\frac{c}{a})^{1}))

= - (ln ((\frac{a}{c})^{5}) + ln ((\frac{c}{a})^{1}))

対数の規則を適用する:

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

ln ((\frac{a}{c})^{5}) + ln ((\frac{c}{a})^{1}) = ln ((\frac{a}{c})^{5} (\frac{c}{a})^{1})

= - ln ((\frac{a}{c})^{5} (\frac{c}{a})^{1})

簡素化

(\frac{a}{c})^{5} (\frac{c}{a})^{1} : \frac{a ^{4}}{c ^{4}}

= - ln (\frac{a ^{4}}{c ^{4}})