簡約 1/2 log_{2(x)}(+2log_{10}(2)(x-6))

解

簡約

\frac{1}{2} lo g_{2 (x)} (+ 2 lo g_{10} (2) (x - 6))

\frac{1}{2} lo g_{2 x} (2) + \frac{1}{2} lo g_{2 x} (lo g_{10} (2)) + \frac{1}{2} lo g_{2 x} (x - 6)

解答ステップ

\frac{1}{2} lo g_{2 (x)} (2 lo g_{10} (2) (x - 6))

規則を適用する:

(a) = a

(x) = x

= \frac{1}{2} lo g_{2 x} (2 lo g_{10} (2) (x - 6))

対数の規則を適用する:

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

lo g_{2 x} (2 lo g_{10} (2) (x - 6)) = lo g_{2 x} (2) + lo g_{2 x} (lo g_{10} (2)) + lo g_{2 x} (x - 6)

= \frac{1}{2} (lo g_{2 x} (2) + lo g_{2 x} (lo g_{10} (2)) + lo g_{2 x} (x - 6))

分配法則を適用する:

m (a + b + c) = ma + mb + m c

\frac{1}{2} (lo g_{2 x} (2) + lo g_{2 x} (lo g_{10} (2)) + lo g_{2 x} (x - 6)) = \frac{1}{2} lo g_{2 x} (2) + \frac{1}{2} lo g_{2 x} (lo g_{10} (2)) + \frac{1}{2} lo g_{2 x} (x - 6)

= \frac{1}{2} lo g_{2 x} (2) + \frac{1}{2} lo g_{2 x} (lo g_{10} (2)) + \frac{1}{2} lo g_{2 x} (x - 6)