簡約 log_{sqrt(2)}(8x)

解

簡約

lo g_{2} (8 x)

6 + 2 lo g_{2} (x)

解答ステップ

lo g_{2} (8 x)

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

2 = 2^{\frac{1}{2}}

= lo g_{2^{\frac{1}{2}}} (8 x)

対数の規則を適用する:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{2^{\frac{1}{2}}} (8 x) = \frac{1}{\frac{1}{2}} lo g_{2} (8 x)

= \frac{1}{\frac{1}{2}} lo g_{2} (8 x)

\frac{1}{\frac{1}{2}} = 2

= 2 lo g_{2} (8 x)

簡素化

lo g_{2} (8 x) : 3 + lo g_{2} (x)

= 2 (3 + lo g_{2} (x))

拡張

2 (3 + lo g_{2} (x)) : 6 + 2 lo g_{2} (x)

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