log 數 help me 步驟

VinCY

2013-04-02 5:17 am

要步驟!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

1. 若 logx+1/2logy=1,則y=?

2. 若 log2=p 及 log3=q ,則 log135=?

3. log_a b/log_b a=?

4. 若2^a=10^b 及 5^c=10^d ,其中a和c為非零 , 則b/a+d/c=?

5.下列何者為最小?
80^2500 600^2000 10000^1500 3000^1000

回答 (1)

用戶2053

2013-04-03 6:02 am

✔ 最佳答案

1)log x + (1/2)log y = 1
(1/2)log y = 1 - log x
log √y = log 10 - log x
log √y = log (10/x)
√y = 10/x
y = 100/x²
2) log 135
= log (3³ * 10/2)
= log 3³ + log (10/2)
= 3log 3 + log 10 - log 2
= 3q + 1 - p
3)logₐ b / logb a
= (log b / log a) / (log a / log b)
= (log b / log a) (log b / log a)
= (log b / log a)²
= (logₐ b)²
4) 2ᵃ = 10ᵇ 及 5ᶜ = 10ᵈ
alog2 = blog10 及 clog5 = dlog10
b/a = log2 及 d/c = log5
∴
b/a + d/c
= log2 + log5
= log(2*5)
= log10
= 1
5)80^2500 = (80^5)^500 > ( (8²)^5 )^500 = ( (8^5)² )^500 = (32768²)^500
600^2000 = (600^4)^500 = (360000²)^500
10000^1500 = (10000³)^500 = (1000000²)^500
3000^1000 = (3000²)^500∵ 3000 < 32768 < 360000 < 1000000
∴ 3000^1000 為最小

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