Re: [中學] 對數問題

[deepwoody (快回火星吧)]

※ 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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