簡約 (ln(n)-2ln(Θ))/(2ln(n))

解

簡約

\frac{ln ( n ) - 2 ln ( Θ )}{2 ln ( n )}

\frac{ln ( \frac{n}{Θ ^{2}} )}{2 ln ( n )}

解答ステップ

\frac{ln ( n ) - 2 ln ( Θ )}{2 ln ( n )}

対数の規則を適用する:

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

2 ln (Θ) = ln (Θ^{2})

= \frac{ln ( n ) - ln ( Θ ^{2} )}{2 ln ( n )}

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 (n) - ln (Θ^{2}) = ln (\frac{n}{Θ ^{2}})

= \frac{ln ( \frac{n}{Θ ^{2}} )}{2 ln ( n )}