簡約 1/2 [log_{10}(2x)+log_{10}(2)(x+1)]

解

簡約

\frac{1}{2} [lo g_{10} (2 x) + lo g_{10} (2) (x + 1)]

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

解答ステップ

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

対数の規則を適用する:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

lo g_{10} (2) (x + 1) = lo g_{10} (2^{x + 1})

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

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} (2 x) + lo g_{10} (2^{x + 1}) = lo g_{10} (2 x \cdot 2^{x + 1})

= \frac{1}{2} lo g_{10} (2 x \cdot 2^{x + 1})

簡素化

2 \cdot 2^{x + 1} : 2^{x + 2}

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