if x = 444.....444 (100 digits), find the value of log x correct to the nearest integer?
A.44
B.99
C.100
D.101
How to calculate?
show steps.
maths question
2014-01-18 11:11 pm
回答 (2)
2014-01-19 10:05 am
✔ 最佳答案
log2 = 0.3010log 3 = 0.4771
log x
= log [444.....444 (100 digits)]
≒ log (0.4444...... x 10^100)
= log (0.4444......) + log (10^100)
= log (4/9) + 100 log (10)
= log 4 - log 9 + 100
= log 2^2 - log 3^2 + 100
= 2 log 2 - 2 log 3 + 100
= 2 x (0.3010) - 2 x (0.4771) + 100
= 99.6478
≒ 100 (to nearest integer)
2014-01-19 02:06:51 補充：
The key step is how to find log (0.4444.....) or log (4.4444......).
2014-01-19 02:07:32 補充：
So, the answer is : (C) 100
2014-01-19 02:08:00 補充：
The key step is how to find log (0.4444.....) or log (4.4444......).
參考: sioieng, sioieng, sioieng
2014-01-18 11:34 pm
x = 444.....444 (100 digits) = 4.44444....X10⁹⁹
logx = log(4.44444....X10⁹⁹) = log(4.444444....) + log(10⁹⁹)
= 0.6478 + 99 = 99.6478
ANS : C
logx = log(4.44444....X10⁹⁹) = log(4.444444....) + log(10⁹⁹)
= 0.6478 + 99 = 99.6478
ANS : C
收錄日期: 2021-04-27 20:33:36
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20140118000051KK00080