若 p = log 3 及 q = log 5 , 試以 p 和 q 表示下列各式
[a] log 75
[b] log 開方75
[c] log 0.15
咁應該點樣用3同5拆開上面既3題數呢!? 請詳細解釋
更新1:
咁如果 p = log 3, q=log5 [f] log6 [g] log12 應該點計!? 如果可以請盡量以：◇五☆dicky★理◇兄既方法解答 又或者：◇五☆dicky★理◇兄見到既話都可以答一答
關於log既問題..
2007-09-16 12:34 am
我有的野唔明, 或者我舉個例先:
若 p = log 3 及 q = log 5 , 試以 p 和 q 表示下列各式
[a] log 75
[b] log 開方75
[c] log 0.15
咁應該點樣用3同5拆開上面既3題數呢!? 請詳細解釋
若 p = log 3 及 q = log 5 , 試以 p 和 q 表示下列各式
[a] log 75
[b] log 開方75
[c] log 0.15
咁應該點樣用3同5拆開上面既3題數呢!? 請詳細解釋
回答 (4)
2007-09-16 7:13 pm
✔ 最佳答案
(a) log75= log(3*5*5)←因為75=3*5*5(方法係當佢叫你以p = log 3及q = log 5表示時試下將75除3或5直至除唔到)
=log3 + log5 +log5←利用公式log (a*b)=log a + log b
=p+2q←代番pq入log 3 log 5
(b) log開方75
=log 75^0.5←開方75=75ge0.5次方
=0.5log 75←利用公式log a^b=b log a
=0.5(p+2q)←因為a已經計到log 75=p+2q,所以可以直接代入
=0.5p + q←化簡
(c) log 0.15
=log(0.01*3*5)←同a一樣方法
=log0.01+log3+log5
=p+q-2
參考: 我
2007-09-16 12:47 am
a). log 75= log(3*25)
= log ( 3*5*5)
= log 3 + log 5 + log 5
=p + 2q
b). log 開方75 = log (75)^1/2
= 1/2* log (75)
= 1/2(p+2q) from part (a)
c). log 0.15= log (0.3*0.5)
= log (3*5/100)
= log 3 +log 5 - log 100
= p+q -2
= log ( 3*5*5)
= log 3 + log 5 + log 5
=p + 2q
b). log 開方75 = log (75)^1/2
= 1/2* log (75)
= 1/2(p+2q) from part (a)
c). log 0.15= log (0.3*0.5)
= log (3*5/100)
= log 3 +log 5 - log 100
= p+q -2
參考: me
2007-09-16 12:45 am
(a)
log 75= log (3X5X5)
From log(M*N) = log M+log N
Hence log 75= log 3+log5 +log5
= p+q+q
= p+2q
(b)
log 開方75 = log (75) ^1/2
From log M^n = n log M
Hence
log 開方75 = 1/2 log 75
From (a)
log 75 = p+2q
Then
log 開方75 = 1/2 log 75
= 1/2 (p+2q)
= 1/2 (p) + q
(c) log 0.15 = log 15 /100
From log M/N = log M - log N
log 0.15 = log 15/100
= log 15 -log 100
= log (3X5) - log 100
= log 3 + log 5 - log 100
= p+ q -2
log 75= log (3X5X5)
From log(M*N) = log M+log N
Hence log 75= log 3+log5 +log5
= p+q+q
= p+2q
(b)
log 開方75 = log (75) ^1/2
From log M^n = n log M
Hence
log 開方75 = 1/2 log 75
From (a)
log 75 = p+2q
Then
log 開方75 = 1/2 log 75
= 1/2 (p+2q)
= 1/2 (p) + q
(c) log 0.15 = log 15 /100
From log M/N = log M - log N
log 0.15 = log 15/100
= log 15 -log 100
= log (3X5) - log 100
= log 3 + log 5 - log 100
= p+ q -2
參考: 自己計的..
2007-09-16 12:42 am
a. log75
= log(3*5*5)
=log3 + log5 +log5
=p+2q
b. log開方75
=log 75^0.5
=0.5log 75
=0.5(p+2q) (from a)
c. log 0.15
=log(0.01*3*5)
=log0.01+log3+log5
=p+q-2
= log(3*5*5)
=log3 + log5 +log5
=p+2q
b. log開方75
=log 75^0.5
=0.5log 75
=0.5(p+2q) (from a)
c. log 0.15
=log(0.01*3*5)
=log0.01+log3+log5
=p+q-2
收錄日期: 2021-05-01 15:42:04
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070915000051KK03202