簡約 1/7 [log_{10}(x)-log_{10}(x+4)]

解

簡約

\frac{1}{7} [lo g_{10} (x) - lo g_{10} (x + 4)]

\frac{lo g _{10} ( \frac{x}{x + 4} )}{7}

解答ステップ

\frac{1}{7} (lo g_{10} (x) - lo g_{10} (x + 4))

対数の規則を適用する:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (x) - lo g_{10} (x + 4) = lo g_{10} (\frac{x}{x + 4})

= \frac{1}{7} lo g_{10} (\frac{x}{x + 4})

分数の規則を適用する:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot lo g _{10} ( \frac{x}{x + 4} )}{7}

規則を適用する:

1 \cdot a = a

1 \cdot lo g_{10} (\frac{x}{x + 4}) = lo g_{10} (\frac{x}{x + 4})

= \frac{lo g _{10} ( \frac{x}{x + 4} )}{7}