簡約-1/2 ln(1/16)+ln(1/2)

解

簡約

- \frac{1}{2} ln (\frac{1}{16}) + ln (\frac{1}{2})

ln (2)

十進法表記

0.69314 \dots

解答ステップ

- \frac{1}{2} ln (\frac{1}{16}) + ln (\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 (\frac{1}{16}) = ln ((\frac{1}{16})^{\frac{1}{2}})

= - ln ((\frac{1}{16})^{\frac{1}{2}}) + ln (\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}{2}) - ln ((\frac{1}{16})^{\frac{1}{2}}) = ln \frac{\frac{1}{2}}{( \frac{1}{16} ) ^{\frac{1}{2}}}

= ln \frac{\frac{1}{2}}{( \frac{1}{16} ) ^{\frac{1}{2}}}

\frac{\frac{1}{2}}{( \frac{1}{16} ) ^{\frac{1}{2}}} = 2

= ln (2)