簡約 3ln(2)+ln(x-2)-2ln(7)

解

簡約

3 ln (2) + ln (x - 2) - 2 ln (7)

ln (\frac{8 ( x - 2 )}{49})

解答ステップ

3 ln (2) + ln (x - 2) - 2 ln (7)

対数の規則を適用する:

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

3 ln (2) = ln (2^{3})

= ln (2^{3}) + ln (x - 2) - 2 ln (7)

対数の規則を適用する:

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

ln (2^{3}) + ln (x - 2) = ln (2^{3} (x - 2))

= ln (2^{3} (x - 2)) - 2 ln (7)

2^{3} = 8

= ln (8 (x - 2)) - 2 ln (7)

対数の規則を適用する:

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

2 ln (7) = ln (7^{2})

= ln (8 (x - 2)) - ln (7^{2})

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 (8 (x - 2)) - ln (7^{2}) = ln (\frac{8 ( x - 2 )}{7 ^{2}})

= ln (\frac{8 ( x - 2 )}{7 ^{2}})

7^{2} = 49

= ln (\frac{8 ( x - 2 )}{49})