Solving the Log Identity Problem: Understanding the Daume Equation

[tahayassen]

Homework Statement

http://img39.imageshack.us/img39/4729/daumequation13275759907.png

Homework Equations

N/A

The Attempt at a Solution

Hmm... This is a tough one. I thought these two functions have been mathematically proven to be exactly the same? Does it have something to do with the domains? The piece-wise function part is totally beyond me. :(

 

[ehild]

Hi tahayassen,

Can you plot log y= (x^2) for negative x values? And y=2log(x)? How can you make them identical?

ehild

 

[tahayassen]

Hi tahayassen,

Can you plot log y= (x^2) for negative x values? And y=2log(x)? How can you make them identical?

ehild

Hmm... I suppose not. I guess for positive x values, I can use 2log(x), and for negative values, I can use 2log(-x) to make it look like log(x^2).

And to make log(x^2) look like 2log(x), I guess I can put the absolute value around the x^2 like so: log(|x^2|). Is this correct?

 

[tahayassen]

No, I've made a mistake

2log(|x|)=log(x^2)
To make log(x^2) look like 2log(x), you would just the positive x values.

 

[tahayassen]

I think I've answered my question.

I just want to confirm if the answer is right:

http://img51.imageshack.us/img51/1087/daumequation13275770432.png

 

[A. Bahat]

Yes, that correct.

 

[ehild]

I think I've answered my question.

I just want to confirm if the answer is right:

http://img51.imageshack.us/img51/1087/daumequation13275770432.png

You did this self-homework-helping job very well Congrats!

ehild