簡約 log_{sqrt(2)}(2sqrt(8))

解

簡約

lo g_{2} (28)

5

解答ステップ

lo g_{2} (28)

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}}} (28)

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}}} (28) = \frac{1}{\frac{1}{2}} lo g_{2} (28)

= \frac{1}{\frac{1}{2}} lo g_{2} (28)

28 = 2^{\frac{5}{2}}

= \frac{1}{\frac{1}{2}} lo g_{2} (2^{\frac{5}{2}})

対数の規則を適用する:

lo g_{a} (a^{b}) = b

lo g_{2} (2^{\frac{5}{2}}) = \frac{5}{2}

= \frac{1}{\frac{1}{2}} \cdot \frac{5}{2}

\frac{1}{\frac{1}{2}} \cdot \frac{5}{2} = 5

= 5