簡約 1/(ln(a)x)(log_{10}(x)+log_{10}(x-7)-1)

解

簡約

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

\frac{lo g _{10} ( x ( x - 7 ) ) - 1}{x ln ( a )}

解答ステップ

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

対数の規則を適用する:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (x) + lo g_{10} (x - 7) = lo g_{10} (x (x - 7))

= \frac{1}{ln ( a ) x} (lo g_{10} (x (x - 7)) - 1)

分数を乗じる:

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

= \frac{1 \cdot ( lo g _{10} ( x ( x - 7 ) ) - 1 )}{ln ( a ) x}

1 \cdot (lo g_{10} (x (x - 7)) - 1) = lo g_{10} (x (x - 7)) - 1

= \frac{lo g _{10} ( x ( x - 7 ) ) - 1}{x ln ( a )}