簡約 10log_{10}((10^{12}0.5)/(4pi*200^2))

解

簡約

10 lo g_{10} (\frac{1 0 ^{12} \cdot 0.5}{4 \cdot π \cdot 20 0 ^{2}})

10 (lo g_{10} (1 0^{12} \cdot 0.5) - lo g_{10} (160000 π))

十進法表記

59.97700 \dots

解答ステップ

10 lo g_{10} (\frac{1 0 ^{12} \cdot 0.5}{4 π 20 0 ^{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)

lo g_{10} (\frac{1 0 ^{12} \cdot 0.5}{4 π 20 0 ^{2}}) = lo g_{10} (1 0^{12} \cdot 0.5) - lo g_{10} (4 π 20 0^{2})

= 10 (lo g_{10} (1 0^{12} \cdot 0.5) - lo g_{10} (20 0^{2} \cdot 4 π))

lo g_{10} (4 π 20 0^{2}) = lo g_{10} (160000 π)

= 10 (lo g_{10} (1 0^{12} \cdot 0.5) - lo g_{10} (160000 π))