Hi,

I was looking at a math book when I stumbled across a problem:

I am a little puzzled. How would I prove it? Using proof by counterexample?Quote:

Prove the following:

given

Thanks!

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- April 9th 2011, 10:02 PMmasougProof of Logarithms
Hi,

I was looking at a math book when I stumbled across a problem:

Quote:

Prove the following:

given

Thanks! - April 9th 2011, 10:05 PMProve It
You can prove this using derivatives...

- April 9th 2011, 10:16 PMmasoug
Okay... Is it possible without derivatives?

- April 9th 2011, 10:29 PMProve It
Why would you want a different method?

First note that for all , while for all . So for all .

Then note that and .

For , we have

So that means grows slower than does, so can never catch up.

Therefore for all . - April 10th 2011, 06:46 PMmasoug
Okay, that makes sense... So we can use growth rates of functions to determine which is the largest in the end.

- April 10th 2011, 07:28 PMKrizalid
Use a contradiction: suppose not, that means that would imply but this is obviously false since