Math Is Fun Forum

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!

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: How do you solve this?

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)

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.

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"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..."