簡約 log_{a^{22a}}(-1/2 (log_{a}(2)+1))

解

簡約

lo g_{a^{22 a}} (- \frac{1}{2} (lo g_{a} (2) + 1))

lo g_{a^{22 a}} (lo g_{a} (2) + 1) - lo g_{a^{22 a}} (2)

解答ステップ

lo g_{a^{22 a}} (- \frac{1}{2} (lo g_{a} (2) + 1))

対数の規則を適用する:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{a^{22 a}} (- \frac{1}{2} (lo g_{a} (2) + 1)) = lo g_{a^{22 a}} (\frac{1}{2}) + lo g_{a^{22 a}} (lo g_{a} (2) + 1)

= lo g_{a^{22 a}} (\frac{1}{2}) + lo g_{a^{22 a}} (lo g_{a} (2) + 1)

対数の規則を適用する:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{a^{22 a}} (\frac{1}{2}) = lo g_{a^{22 a}} (1) - lo g_{a^{22 a}} (2)

= lo g_{a^{22 a}} (1) - lo g_{a^{22 a}} (2) + lo g_{a^{22 a}} (lo g_{a} (2) + 1)

対数の規則を適用する:

lo g_{a} (1) = 0

= 0 - lo g_{a^{22 a}} (2) + lo g_{a^{22 a}} (lo g_{a} (2) + 1)

0 - lo g_{a^{22 a}} (2) + lo g_{a^{22 a}} (lo g_{a} (2) + 1) = - lo g_{a^{22 a}} (2) + lo g_{a^{22 a}} (lo g_{a} (2) + 1)

= lo g_{a^{22 a}} (lo g_{a} (2) + 1) - lo g_{a^{22 a}} (2)