F.4maths對數函數

試不用計數機求下列各式的值。
1)
(1/3) log 27 + (2/3) log 8 - log 20
= (1/3) log 3³ + (2/3) log 2³ - log 20
= (1/3) x 3 log 3 + (2/3) x 3 log 2 - log 20
= log 3 + 2 log 2 - log 20
= log 3 + log 2² -log 20
= log 3 + log 4 - log 20
= log (3 x 4 / 20)
= log 0.6

（不用計算機，只能計至此答案。）


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化簡下列各式，其中x>0，x≠1及y>0。
1)
(log ⁴√x + log x²) / log √x
= [(1/4) log x + 2 log x] / [(1/2) log x]
= (9/4) / (1/2)
= 9/2
= 4.5


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若s = log 2 及 t = log 3，試以s 和 t 表示下列各項。
1a) log 60
b) log (5/9)
c) log 0.45
1a)
log 60
= log (2 x 3 x 10)
= log 2 + log 3 + log 10
= s + t + 1

b)
log (5/9)
= log (10/18)
= log 10 - log 18
= 1 - log (2 x 3 x 3)
= 1 - log 2 - 2 log 3
= 1 - s - 2t

c)
log 0.45
= log (9/20)
= log [(3 x 3) / (2 x 10)]
= 2 log 3 - log 2 - log 10
= 2t - s - 1

你睇下呢兩個 posts:

https://hk.knowledge.yahoo.com/question/question?qid=7014051400058

https://hk.knowledge.yahoo.com/question/question?qid=7014051500040