S6 pure math que.:function(2)

2009-10-05 2:34 am
1) a) prove that (log a^k)x=1/k (log a)x
b) given that n belongs to N,a>1 and a belongs to R, for x,
solve (log a)x-4(log a^2)x +12(log a^3)x+........+n(-2)^(n-1) (log a^n)x > (1-(-2)^n)/3 (loga)(x^2 - a)

2) given that f(x+1/x)=x^2+ 1/(x^2), find f(x)


if the answer have steps, pls give the steps to me as long as u can,thank you so much!!
更新1:

in Q 1)a), "a^k" and "a" are the base of log Q 1)b) both "a","a^2","a^3","a^n" are the base of log! sorry for the unclear expression! thank you very much@!

回答 (2)

2009-10-05 4:14 am
✔ 最佳答案
1(a) log a^k x
=logx/log a^k
=logx/k log a
=(1/k) loga x
(b) (log a)x-4(log a^2)x +12(log a^3)x+........+n(-2)^(n-1) (log a^n)x
=logx/loga-4logx/2loga+12logx/3loga+...+n(-2)^(n-1) logx/nloga
=[1-2+2^2-...+(-2)^(n-1)][logx/loga]
=[1-(-2)^n]/[3][logx/loga]
I think you have some typing error on the R.H.S.
2 f(x+1/x)=x^2+ 1/(x^2),
Let y=x+1/x=>y^2=x^2+2+1/x^2
So x^2+1/x^2=y^2-2
That is f(y)=y^2-2 or f(x)=x^2-2
2009-10-05 3:52 am
(log a^k)x=(1/k)(log a)x??


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