Given that log 底數2 3 = a and log 底數2 5 = b, express the following in terms of a and b.
(a) log底數2 0.15
(b) log底數2 開方270
1Q (LOG aribitrary base)
2009-12-08 3:42 am
回答 (2)
2009-12-08 4:39 am
✔ 最佳答案
a)log(b2) 0.15= log(b2) (3/20)
= log(b2) 3 - log(b2) [(2^2) * 5]
= log(b2) 3 - 2log(b2) 2 - log(b2) 5
= a - 2 - b
= a - b - 2
b) log(b2) (270^0.5)
= 0.5 log(b2) [(3^3) * 2 * 5)]
= 0.5 [ 3log(b2) 3 + log(b2) 2 + log(b2) 5]
= 0.5 * (3a + 1 + b)
= (3a + b + 1)/2
2009-12-08 4:41 am
a) log 0.15=log 3/20=log 3 -log 20=a-log 2x2x5
=a- (log 2+log 2+log 5)=a-1-1-b=a-b-2
b) log 開方270=1/2 log 270=1/2 log(2x3x3x3x5)
=1/2( log2+log3+log3+log3+log5)=1/2(1+a+a+a+b)=3/2a+1/2b+1/2
All log are log底數2
=a- (log 2+log 2+log 5)=a-1-1-b=a-b-2
b) log 開方270=1/2 log 270=1/2 log(2x3x3x3x5)
=1/2( log2+log3+log3+log3+log5)=1/2(1+a+a+a+b)=3/2a+1/2b+1/2
All log are log底數2
參考: ME
收錄日期: 2021-04-21 22:06:30
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https://hk.answers.yahoo.com/question/index?qid=20091207000051KK01234