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How does this simplify to give this answer?

  1. Mar 2, 2013 #1
    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. jcsd
  3. Mar 2, 2013 #2

    Dick

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    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
  4. Mar 2, 2013 #3

    SammyS

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


    To answer your primary question:

    Use the following logarithm property.
    [itex]\displaystyle C\cdot\ln(u)=\ln(u^C\,) [/itex]​
     
  5. Mar 2, 2013 #4
    ...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:

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

    Shoud become this:

    [itex]\pi[/itex][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?
    Please help.
    Thank you so much! :)
     
  6. Mar 2, 2013 #5

    Dick

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    If your question is why (2/√(2))=√(2), none of that has much to do with it. Did you miss my post?
     
  7. Mar 2, 2013 #6

    SammyS

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    Did you know that [itex]\displaystyle \ \ \frac{2}{\sqrt{2}} = \sqrt{2}\ ?[/itex]

    Furthermore, [itex]\displaystyle \ (\sqrt{2}\,)^2=2\ .[/itex]
     
  8. Mar 2, 2013 #7
    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! :/
     
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