設a>0,b>0,a≠1,b≠1,
化簡
(log a ab)(log b ab)-(log a b+log b a)
問數~關於對數計算~
2008-02-11 7:12 am
回答 (1)
2008-02-11 7:28 am
✔ 最佳答案
(loga ab)(logb ab) - (loga b + logb a)= (loga a + loga b)(logb a + logb b) - loga b - logb a
= (1 + loga b)(logb a + 1) - loga b - logb a
= logb a + loga b logb a + 1 + loga b - loga b - logb a
= loga b logb a + 1
= 1 + 1
= 2
Note: Let b = ac
loga b = c
But b1/c = a
logb a = 1/c
Hence, loga b logb a = 1
收錄日期: 2021-04-13 15:07:10
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080210000051KK03453