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#1 2007-05-05 09:08:15

jdo42424
Member
Registered: 2007-05-05
Posts: 0

Arithmetic Sequence, need answer badly

log 1000, log100, log 10, log 1,.......

Need to find the N th term

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#2 2007-05-08 02:33:32

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Arithmetic Sequence, need answer badly

If you change those terms into actual numbers, it becomes very simple to see what the nth term is.

log 1000, log 100, log 10, log 1, ...
becomes
3, 2, 1, 0, ...

So the nth term is clearly 4-n.
If for some reason you want it in terms of logs, then it would be log [10000/(10^n)].


Why did the vector cross the road?
It wanted to be normal.

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#3 2007-05-08 04:33:18

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Arithmetic Sequence, need answer badly

To see it in a different way, log base 10 is a function which counts the number of 10s which are in a number.  So there are 3 10s in 1000 because log(1000) = 3.  When we divide out by 10, we reduce the number of 10s.  This is why log(1000/10) = log(100) = 2.  The same with log(10), and there are 0 10s in log(1).  So what happens when we divide by 10 again?  log(1/10) = -1, so there are -1 10s in 1/10.  Does this make sense?


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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