簡約 ln(1/(e^{20)}-1)-ln(20)(1/2)

解

簡約

ln (\frac{1}{e ^{20}} - 1) - ln (20) (\frac{1}{2})

ln (\frac{5 ( 1 - e ^{20} )}{10 e ^{20}})

解答ステップ

ln (\frac{1}{e ^{20}} - 1) - ln (20) (\frac{1}{2})

対数の規則を適用する:

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

(\frac{1}{2}) ln (20) = ln (2 0^{(\frac{1}{2})})

= ln (\frac{1}{e ^{20}} - 1) - ln (2 0^{(\frac{1}{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 (\frac{1}{e ^{20}} - 1) - ln (2 0^{(\frac{1}{2})}) = ln (\frac{\frac{1}{e ^{20}} - 1}{2 0 ^{\frac{1}{2}}})

= ln (\frac{\frac{1}{e ^{20}} - 1}{2 0 ^{\frac{1}{2}}})

\frac{\frac{1}{e ^{20}} - 1}{2 0 ^{(\frac{1}{2})}} = \frac{5 ( 1 - e ^{20} )}{10 e ^{20}}

= ln (\frac{5 ( 1 - e ^{20} )}{10 e ^{20}})