急! 有關 log 數變換方法1條

1.
設 25ⁿ = x
根據 log 的定義：n = log25(x)...... [1]

25ⁿ = x
兩邊同時取以 5 為底的 log：log5(25ⁿ) = log5(x)
n log5(25) = log5(x)
n = log5(x) / log5(25) ...... [2]

[1] = [2] :
log­25(x) = log5(x) / log5(25)

較快的方法是利用公式：logm(n) = logy(n) / logy(m)­
令 m = 25, n = x 及 y = 5


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2.
log5(25)
= log5(5²)
= 2 log5(5)
= 2 ................. (由於 log5(5) = 1)

代入 log5(25) = 2：
log5(x) / log5(25) = log5(x) / 2
所以 log5(x) / log5(25) = (1/2)log5(x)

andrew，很久不見了～ ^__^