簡約 ln((a^1)/(b^1c^{-1)})

解

簡約

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

ln (a) - ln (b) + ln (c)

解答ステップ

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

= ln (a^{1}) - ln (b^{1} c^{- 1})

対数の規則を適用する:

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

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

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

対数の規則を適用する:

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

ln (b^{1} c^{- 1}) = ln (b^{1}) + ln (c^{- 1})

= 1 \cdot ln (a) - (ln (b^{1}) + ln (c^{- 1}))

対数の規則を適用する:

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

ln (b^{1}) = 1 \cdot ln (b)

= 1 \cdot ln (a) - (1 \cdot ln (b) + ln (c^{- 1}))

対数の規則を適用する:

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

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

= 1 \cdot ln (a) - (1 \cdot ln (b) - 1 \cdot ln (c))

1 \cdot ln (a) = ln (a)

- (1 \cdot ln (b) - 1 \cdot ln (c)) = - (ln (b) - ln (c))

= ln (a) - (ln (b) - ln (c))

- (ln (b) - ln (c)) : - ln (b) + ln (c)

= ln (a) - ln (b) + ln (c)