簡約 2ln(+ln(c)-3ln(5c))

解

簡約

2 ln (+ ln (c) - 3 ln (5 c))

2 ln (- ln (125 c^{2}))

解答ステップ

2 ln (ln (c) - 3 ln (5 c))

対数の規則を適用する:

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

3 ln (5 c) = ln ((5 c)^{3})

= 2 ln (ln (c) - ln ((5 c)^{3}))

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 (c) - ln ((5 c)^{3}) = ln (\frac{c}{( 5 c ) ^{3}})

= 2 ln (ln (\frac{c}{( 5 c ) ^{3}}))

簡素化

\frac{c}{( 5 c ) ^{3}} : \frac{1}{125 c ^{2}}

= 2 ln (ln (\frac{1}{125 c ^{2}}))

簡素化

ln (\frac{1}{125 c ^{2}}) : - ln (125 c^{2})

= 2 ln (- ln (125 c^{2}))