簡約 ln(1/(2pi(x^2)^{n/2)})

解

簡約

ln (\frac{1}{2 π ( x ^{2} ) ^{\frac{n}{2}}})

- \frac{n ln ( x ^{2} )}{2} - ln (2) - ln (π)

解答ステップ

ln (\frac{1}{2 π ( x ^{2} ) ^{\frac{n}{2}}})

対数の規則を適用する:

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

ln (\frac{1}{2 π ( x ^{2} ) ^{\frac{n}{2}}}) = ln (1) - ln (2 π (x^{2})^{\frac{n}{2}})

= ln (1) - ln (2 π (x^{2})^{\frac{n}{2}})

対数の規則を適用する:

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

ln (2 π (x^{2})^{\frac{n}{2}}) = ln (2) + ln (π) + ln ((x^{2})^{\frac{n}{2}})

= ln (1) - (ln ((x^{2})^{\frac{n}{2}}) + ln (2) + ln (π))

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= ln (1) - (ln (2) + ln (π) + \frac{n}{2} ln (x^{2}))

対数の規則を適用する:

lo g_{a} (1) = 0

= 0 - (\frac{n}{2} ln (x^{2}) + ln (2) + ln (π))

乗じる

\frac{n}{2} ln (x^{2}) : \frac{n ln ( x ^{2} )}{2}

= 0 - (\frac{n ln ( x ^{2} )}{2} + ln (2) + ln (π))

0 - (ln (2) + ln (π) + \frac{n ln ( x ^{2} )}{2}) = - (ln (2) + ln (π) + \frac{n ln ( x ^{2} )}{2})

= - (\frac{n ln ( x ^{2} )}{2} + ln (2) + ln (π))

括弧を分配する

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

マイナス・プラスの規則を適用する

+ (- a) = - a

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