簡約 20log_{10}((4pi)/(1/8))-20log_{10}(0.5)

解

簡約

20 lo g_{10} (\frac{4 π}{\frac{1}{8}}) - 20 lo g_{10} (0.5)

lo g_{10} (1.16573 E 46)

十進法表記

46.06659 \dots

解答ステップ

20 lo g_{10} (\frac{4 π}{\frac{1}{8}}) - 20 lo g_{10} (0.5)

対数の規則を適用する:

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

20 lo g_{10} (\frac{4 π}{\frac{1}{8}}) = lo g_{10} ((\frac{4 π}{\frac{1}{8}})^{20})

= lo g_{10} ((\frac{4 π}{\frac{1}{8}})^{20}) - 20 lo g_{10} (0.5)

対数の規則を適用する:

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

20 lo g_{10} (0.5) = lo g_{10} (0. 5^{20})

= lo g_{10} ((\frac{4 π}{\frac{1}{8}})^{20}) - lo g_{10} (0. 5^{20})

対数の規則を適用する:

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

lo g_{10} ((\frac{4 π}{\frac{1}{8}})^{20}) - lo g_{10} (0. 5^{20}) = lo g_{10} \frac{( \frac{4 π}{\frac{1}{8}} ) ^{20}}{0. 5 ^{20}}

= lo g_{10} \frac{( \frac{4 π}{\frac{1}{8}} ) ^{20}}{0. 5 ^{20}}

\frac{( \frac{4 π}{\frac{1}{8}} ) ^{20}}{0. 5 ^{20}} = 1.16573 E 46

= lo g_{10} (1.16573 E 46)