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Log Identity Problem

  1. Jan 26, 2012 #1
    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. jcsd
  3. Jan 26, 2012 #2

    ehild

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    Gold Member

    Hi tahayassen,

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

    ehild
     
  4. Jan 26, 2012 #3
    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?
     
  5. Jan 26, 2012 #4
    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.
     
  6. Jan 26, 2012 #5
    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
  7. Jan 26, 2012 #6
    Yes, that correct.
     
  8. Jan 26, 2012 #7

    ehild

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

    ehild
     
    Last edited by a moderator: May 5, 2017
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