Form4 maths question about logarithmic functions(1)

用戶22906

2008-10-28 3:25 pm

18.
9^(x-2)=4^(3-2x)
23.Simplify log(100y)/(1+√y)
24(a).Simplify (a^3 +b^3)/(a-b)^2
(b)Hence evaluate log[(72^3+ 28^3)/(72-28)^2]
25. If 1/3log x=12,
find (a)log(10x)
(b)2logx
Ans:18. 1.72
23. 2
24(a) a+b
(b)6
25.(a) 37
(b)72
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更新1:

24題打錯，係a^3+b^3/a^2-ab+b^2

更新2:

23題巳經搞店，係2= = log(100y)/1+log√y =log100+logy/log10+0.5logy =2(log10+0.5logy)/log10+0.5logy =2

回答 (1)

用戶10012

2008-10-28 6:28 pm

✔ 最佳答案

18.
9^(x-2) = 4^(3-2x)
(x-2)log 9 = (3-2x) log 4
x log 9 - 2log 9 = 3 log 4 - 2x log 4
x(log 9 + 2 log 4) = 3 log 4 + 2 log 9
x = (3log 4 + 2 log 9)/(log 9 + 2 log 4)
= (log 64 + log 81)/(log 9 + log 16)
= log 5184/log 144 = 3.71466/2.1584 = 1.721.
23.
Since log 100 = 2, you said the answer is 2, that means answer is independent of the value of y which seems not possible, when y = 1, it is log 100/2, when y = 4, it is log 400/3.
24. Since (a - b)^2 is not equal to a^2 - ab + b^2, answer cannot be a +b. Take a = 2 and b = 1, (2^3 + 1^3)/(2-1)^2 = 9 which is not equal to 3.
25.
1/3 log x = 12
so log x = 36.
log (10x) = log 10 + log x = 1 + 36 = 37.
2log x = 2(36) = 72.

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