Re: [中學] 對數問題

[freePrester (Prester)]

※ 引述《iverson3hi (阿輝)》之銘言：
: http://i.imgur.com/x6RBzgH.jpg


(log x + log 2)(log x + log 3) = 1

       2
(log x)  + (log 2 + log 3)log x + (log 2)(log 3) - 1 = 0

                         2
令 log x = t 、 原式 => t  + (log 6)t + (log 2)(log 3) - 1 = 0

得 t 的兩根 t1 = log a 、 t2 = log b

由根與係數關係

t1 + t2 = -log 6 = log a + log b

                1
log (ab) = log ---
                6

           1
所以 ab = ---
           6

: http://i.imgur.com/zsYyJvE.jpg

 3  2                (-3/2)
a  b  = 1   =>  b = a

                3
所以 log b = - ---
        a       2

    /  2  3\                    5
log | a  b |  = 2 + 3log b = - ---
   a\      /                    2

: 請問各位～這兩題的對數題目要如何解呢謝謝～



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※ 編輯: freePrester (1.169.251.167), 12/16/2016 16:50:41
推 iverson3hi  : 非常謝謝您～