有關指數、對數的題目有幾題不知道要怎麼算，拜託各位大大幫幫我

[匿名]

2013-12-29 6:55 pm

1. 若log x=3.3010，試求下列各數的首數及尾數：
(1) log 10x 答：首數=4,尾數=0.3010
(2) log(x/100) 答：首數=1,尾數=0.3010

2. 已知log2=0.3010，log3=0.4771，試求下列各數的近似值：
(1) log12 答：1.0791
(2) log60 答：1.7781
(3) log0.0081 答：-2.0916

3. f(x)=2^x，f(a)=3且f(b)=5，則f(a+b)=？
答：15
4. 試求對數方程式log_10[x^log_10(x)] - 2log_10(x) +1 =0 的解？
註： _ 是指底數的意思，例如：前面的log的底數是10, 真數是x^log_10(x)
答：10
5. 已知log2=0.3010、log3=0.4771，那麼log30=？
答：1.4771
6. 已知log x=5.5105，那麼log 100x 的首數為多少？
答：7

7. 利用查表方式求下個真數x得近似值：
(1) log x=0.8603 答：x=7.25
(2) log x=2.6314 答：x=428
(3) log x=-2.266 答：x=0.00542
(4) log x=2.6201[小數點前面的2上面有一條橫線，後面的2沒有] 答：x=0.0417

回答 (1)

fooks

2013-12-29 7:33 pm

✔ 最佳答案

1.
(1)
log 10x
= log 10 + log x
= 1 + 3.3010
= 4.3010

首數 = 4 及尾數 = 0.3010

(2)
log (x/100)
= log x - log 100
= 3.3010 - 2
= 1.3010

首數 = 1 及尾數 = 0.3010

2.
(1)
log 12
= log (2² x 3)
= 2 log 2 + log 3
= 2 x 0.3010 + 0.4771
= 1.0791

(2)
log 60
= log (10 x 2 x 3)
= log 10 + log 2 + log 3
= 1 + 0.3010 + 0.4771
= 1.7781

(3)
log 0.0081
= log (3⁴ / 10000)
= 4 log 3 - log 10000
= 4 x 0.4771 - 4
= -2.0916

3.
f(a) = 2^a = 3
f(b) = 2^b = 5

f(a + b)
= 2^(a + b)
= 2^a x 2^b
= 3 x 5
= 15

4.
log10 [x^(log10 x)] - 2 (log10 x) + 1 = 0
(log10 x) * (log10 x) - 2 (log10 x) + 1 = 0
(log10 x)² - 2 (log10 x) +1 = 0
[(log10 x) - 1]² = 0
log10 x = 1
x = 10

5.
log 30
= log (10 x 3)
= log 10 + log 3
= 1 + 0.4771
= 1.4771

6.
log 100x
= log 100 + log x
= 2 + 5.5105
= 7.5105

首數 = 7

7.
(1)
antilog 0.8603 = 7.25

(2)
antilog 2.6314 = 428

(3)
antilog (-2.266) = 0.00542

(4)
log 2.6201 [前面 2 為 bar 2] = 0.0417

參考: fooks

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