簡約 log_{4}(log_{3}(9))

解

簡約

lo g_{4} (lo g_{3} (9))

\frac{1}{2}

十進法表記

0.5

解答ステップ

lo g_{4} (lo g_{3} (9))

数を因数に分解する:

4 = 2^{2}

= lo g_{2^{2}} (lo g_{3} (9))

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^{2}} (lo g_{3} (9)) = \frac{1}{2} lo g_{2} (lo g_{3} (9))

= \frac{1}{2} lo g_{2} (lo g_{3} (9))

lo g_{3} (9) = 2

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

対数の規則を適用する:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

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

数を乗じる:

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

= \frac{1}{2}