簡約 20log_{10}((4pi*30)/(300/175))

解

簡約

20 \cdot lo g_{10} (\frac{4 \cdot π \cdot 30}{\frac{300}{175}})

20 (lo g_{10} (120 π) - lo g_{10} (\frac{12}{7}))

十進法表記

46.84495 \dots

解答ステップ

20 lo g_{10} (\frac{4 π 30}{\frac{300}{175}})

対数の規則を適用する:

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

lo g_{10} (\frac{4 π 30}{\frac{300}{175}}) = lo g_{10} (4 π 30) - lo g_{10} (\frac{300}{175})

= 20 (lo g_{10} (4 \cdot 30 π) - lo g_{10} (\frac{300}{175}))

数を乗じる:

4 \cdot 30 = 120

= 20 (lo g_{10} (120 π) - lo g_{10} (\frac{300}{175}))

\frac{300}{175} = \frac{12}{7}

= 20 (lo g_{10} (120 π) - lo g_{10} (\frac{12}{7}))