簡約 (10000)/(200pi^2)(ln((400)/(0.4))+ln(8))

解

簡約

\frac{10000}{200 π ^{2}} (ln (\frac{400}{0.4}) + ln (8))

\frac{150 ln ( 20 )}{π ^{2}}

十進法表記

45.52967 \dots

解答ステップ

\frac{10000}{200 π ^{2}} (ln (\frac{400}{0.4}) + ln (8))

対数の規則を適用する:

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

ln (\frac{400}{0.4}) + ln (8) = ln (8 \cdot \frac{400}{0.4})

= \frac{10000}{200 π ^{2}} ln (8 \cdot \frac{400}{0.4})

\frac{400}{0.4} \cdot 8 = 8000

= \frac{10000}{200 π ^{2}} ln (8000)

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{10000 ln ( 8000 )}{200 π ^{2}}

数を割る:

\frac{10000}{200} = 50

= \frac{50 ln ( 8000 )}{π ^{2}}

簡素化

ln (8000) : 3 ln (20)

= \frac{50 \cdot 3 ln ( 20 )}{π ^{2}}

数を乗じる:

50 \cdot 3 = 150

= \frac{150 ln ( 20 )}{π ^{2}}