簡約 1/2 (ln(2)+2ln(x)+5ln(m)-H)

解

簡約

\frac{1}{2} (ln (2) + 2 ln (x) + 5 ln (m) - H)

\frac{1}{2} (ln (2 x^{2} m^{5}) - H)

解答ステップ

\frac{1}{2} (ln (2) + 2 ln (x) + 5 ln (m) - H)

対数の規則を適用する:

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

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

= \frac{1}{2} (ln (x^{2}) + 5 ln (m) + ln (2) - H)

対数の規則を適用する:

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

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

= \frac{1}{2} (ln (2 x^{2}) + 5 ln (m) - H)

対数の規則を適用する:

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

5 ln (m) = ln (m^{5})

= \frac{1}{2} (ln (2 x^{2}) + ln (m^{5}) - H)

対数の規則を適用する:

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

ln (2 x^{2}) + ln (m^{5}) = ln (2 x^{2} m^{5})

= \frac{1}{2} (ln (2 x^{2} m^{5}) - H)