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#1 2009-02-07 04:14:19

freddogtgj
Member
Registered: 2006-12-02
Posts: 54

How do you solve this?

I'm having trouble with this question, can you help?


Need to find n.

Thanks in advance!

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#2 2009-02-07 07:36:58

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: How do you solve this?

JaneFairfax wrote:

Are you sure, Jane?

Plot of x^2+2x vs 2^x+3

n>5 also works.

Last edited by Daniel123 (2009-02-07 07:40:32)

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#3 2009-02-08 04:39:22

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

Re: How do you solve this?

You can solve the general cases by comparisons of growth.  For example, 2^n grows much faster than n^2, so eventually the RHS will always win in the positive numbers.  For negative integers, the RHS becomes smaller than 3, while the LHS is dominated by the n^2 term which will give high positive numbers.  All that remains is to see where this domination happens, and figure out all the cases in between them.


"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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