# Log Identity Problem

1. Jan 26, 2012

### tahayassen

1. The problem statement, all variables and given/known data

http://img39.imageshack.us/img39/4729/daumequation13275759907.png [Broken]

2. Relevant equations

N/A

3. 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. :(

Last edited by a moderator: May 5, 2017
2. Jan 26, 2012

### 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

3. Jan 26, 2012

### tahayassen

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?

4. Jan 26, 2012

### tahayassen

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

5. Jan 26, 2012

### 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 [Broken]

Last edited by a moderator: May 5, 2017
6. Jan 26, 2012

### A. Bahat

Yes, that correct.

7. Jan 26, 2012

### ehild

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

ehild

Last edited by a moderator: May 5, 2017