簡約 1/12 (log_{10}(3/4)+log_{10}(5/4))

解

簡約

\frac{1}{12} (lo g_{10} (\frac{3}{4}) + lo g_{10} (\frac{5}{4}))

\frac{1}{12} lo g_{10} (\frac{15}{16})

十進法表記

- 0.00233 \dots

解答ステップ

\frac{1}{12} (lo g_{10} (\frac{3}{4}) + lo g_{10} (\frac{5}{4}))

対数の規則を適用する:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (\frac{3}{4}) + lo g_{10} (\frac{5}{4}) = lo g_{10} (\frac{3}{4} \cdot \frac{5}{4})

= \frac{1}{12} lo g_{10} (\frac{3}{4} \cdot \frac{5}{4})

\frac{3}{4} \cdot \frac{5}{4} = \frac{15}{16}

= \frac{1}{12} lo g_{10} (\frac{15}{16})