# How does this simplify to give this answer?

1. Mar 2, 2013

### Lo.Lee.Ta.

1. I am on the very last step of this problem, but I don't see how this equation simplifies from
2ln|(2/√(2)) + 1| - 2ln|1 + 0| to 2ln|√(2) + 1|.

2. I thought that since ln|1| = 0, then 2x0=0. And then the answer would be:
2ln|2/√(2) +1|.

I don't see how the 2 in the (2/√(2)) was canceled out to give just √(2)...

Would you please explain this to me?
Thank you very much! :D

2. Mar 2, 2013

### Dick

2=(√2)*(√2). Or 2=2^1, √2=2^(1/2). (2^1)/(2^(1/2))=2^(1-1/2)=2^(1/2).

Last edited: Mar 2, 2013
3. Mar 2, 2013

### SammyS

Staff Emeritus
Comment #1: Those are not equations -- there are no equal signs.

Use the following logarithm property.
$\displaystyle C\cdot\ln(u)=\ln(u^C\,)$​

4. Mar 2, 2013

### Lo.Lee.Ta.

...I was debating using the word "equation," but then I didn't know what else to call it... :/
Thanks, though! :)
I didn't even know that was a property. Thanks! Will remember!

So then this:

$\pi$[2ln|(2/√(2)) + 1|) - $\pi$[2ln|1|]

Shoud become this:

$\pi$[ln|(2/√(2)) + 1|2] - 0

From the property: C*ln(u) = ln(uC), it seems that the entire [(2/√(2)) + 1] is the u...

But that does not seem to be correct because then that squared would be:

(4/√(2)) + 3...

So I guess only the (2/√(2)) is considered the u...???

But then that would equal ln|2 + 1| = ln|3|

I don't see how the √(2) remains.

Am I saying the u equals the wrong thing?
Thank you so much! :)

5. Mar 2, 2013

### Dick

If your question is why (2/√(2))=√(2), none of that has much to do with it. Did you miss my post?

6. Mar 2, 2013

### SammyS

Staff Emeritus
Did you know that $\displaystyle \ \ \frac{2}{\sqrt{2}} = \sqrt{2}\ ?$

Furthermore, $\displaystyle \ (\sqrt{2}\,)^2=2\ .$

7. Mar 2, 2013

### Lo.Lee.Ta.

Oh, wow, you guys! XD

Yes, Dick, I did miss your post! When I was scrolling through, I seemed to only see SammyS's!

Wow, √(2)/2 = √(2)!!!!! Ugh, okay! ;)

I get it now! Thanks, Dick and SammyS! :D
simple mistake! :/