Math Is Fun Forum

NumOne

Member

Registered: 2012-01-16

Posts: 9

How to expand logarithms

Hi

I have the following statement

2^(⌊lg n⌋+⌈lg n⌉)∕n ∈ Θ(n)

I need to prove it. The first thing that I am going to do is to expand the exponential .. someone gave me a hint about expanding the exponential but I didn't understand it.

Can someone explain that to me plz ?

Thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: How to expand logarithms

Hi NumOne;

Mind if I see the hint?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

NumOne

Member

Registered: 2012-01-16

Posts: 9

Re: How to expand logarithms

n1*n2/n, where n1<=n<=n2, 2*n1>n and n*2>n2

Located on StackOverFlow.com
How to Prove Asymptotic Notations

It's complicated !!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: How to expand logarithms

Hi NumOne;

I am there now and I do not understand it either. I am sorry about that.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: How to expand logarithms

I'm assuming lg means the base 2 logarithm.

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Wrap it in bacon