作者deepwoody (快回火星吧)
看板Math
標題Re: [中學] 對數問題
時間Tue Jan 18 11:14:58 2011
※ 引述《antpo (喵喵)》之銘言：
: 請高手協助解兩題對數問題
: 感激不盡~ ^^
: 1. X和333的對數尾數相同,且10^-3 < X <10^-2,試求X的值
: 2. 設log437=2.6405, log43.8=1.6415,若logx= -0.3588,試求x的值
1.
x = a*10^(-3)，1 ≦ a < 10
=> log = -3 + log(a)
log333 = log(3.33*10^2) = 2 + log3.33
尾數相同 => a = 3.33
所以 x = 3.33*10^(-3)
2.
log4.37 = log437 - 2 = 0.6405
log4.38 = log43.8 - 1 = 0.6415
log(10x) = 1-0.3588 = 0.6412
內插法
(0.6412-0.6405)/(0.6415-0.6405) = (10x-4.37)/(4.38-4.37)
=> 0.7 = 10x-4.37/0.01
=> 0.007 = 10x-4.37
=> 10x = 4.377
=> x = 0.4377
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1F：推 antpo :深表感謝~~ :) 01/18 11:18