急急急.....對數函數 log!!!!!!!!!1

用戶87356

2011-01-22 7:19 pm

7(d) log16/log 3開方4(個3係開方左上角).......答案:6

9.若log2=a,以a表示
(c) log 開方2^3.................答案:3/2a

18.其中,a,b>0
2log開方a+loga^4/3log 4開方a(個4係開方左上角)...答案:20/3

20.其中x>0
a) 6+logx^3/log(100x)............答案:3

b)logx-log開方x/logx+log 3開方x(個3係開方左上角).......答案:3/8

回答 (1)

用戶2053

2011-01-22 7:39 pm

✔ 最佳答案

7d)log16 / log ∛4= log 4² / log 4^(1/3)= 2log4 / [(1/3) log4]= 2 / (1/3)= 6
9c)log √2³= log 2^(3/2)= (3/2) log2= (3/2)a
18)(2log√a + log a^4) / [3log a^(1/4)]= [2log a^(1/2) + 4loga] / [(3/4) loga]= (log a + 4loga) / [(3/4) loga]= (5 log a) / [(3/4) loga]= 20/3
20a)(6 + logx³) / log (100x)= (6 + 3logx) / (log 100 + log x)= 3(2 + logx) / (2 + logx)= 3b)(logx - log√x) / (logx + log∛x)= [logx - (1/2)logx] / (logx + (1/3)logx)= (logx)(1 - 1/2) / [logx(1 + 1/3)]= (1 - 1/2) / (1 + 1/3)= (1/2) / (4/3)= 3/8

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