簡約 20*log_{10}((10)/(sqrt(0.24)))

解

簡約

20 \cdot lo g_{10} (\frac{10}{0.24})

20 (1 - \frac{1}{2} lo g_{10} (0.24))

十進法表記

26.19788 \dots

解答ステップ

20 lo g_{10} (\frac{10}{0.24})

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{10}{0.24}) = lo g_{10} (10) - lo g_{10} (0.24)

= 20 (lo g_{10} (10) - lo g_{10} (0.24))

lo g_{10} (10) = 1

lo g_{10} (0.24) = \frac{1}{2} lo g_{10} (0.24)

= 20 (- \frac{1}{2} lo g_{10} (0.24) + 1)