簡約 ln(a+b)+ln(a-b)-4ln(c)

解

簡約

ln (a + b) + ln (a - b) - 4 ln (c)

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

解答ステップ

ln (a + b) + ln (a - b) - 4 ln (c)

対数の規則を適用する:

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

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

= ln ((a + b) (a - b)) - 4 ln (c)

対数の規則を適用する:

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

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

= ln ((a + b) (a - b)) - ln (c^{4})

対数の規則を適用する:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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