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Logarithmic function #2

  1. Jan 17, 2009 #1
    Hello again..

    1. The problem statement, all variables and given/known dataI
    I have to change this to one term only, the valid answer is: log (x + 1)

    The term is: 2 log (x2 - 1) - log (x + 1) - 2 log (x - 1)

    2. Relevant equations
    Logarithmic laws:

    x log n = log nx
    log m - log n = log (m/n)

    3. The attempt at a solution
    I have tried dividing them but I don't see to be getting anywhere or anywhere close at all at the answer, I also tried factorising but I cannot figure it out, I'm pretty sure that it has some factorization (perfect squares? not sure what they're called in english..)

    Thank you in advanced, this forum is a very useful resource!
  2. jcsd
  3. Jan 17, 2009 #2
    So you said you tried dividing. That gives log ( (x2-1)2/((x+1)(x-1)2) ). Now you just need to use the fact that (x2-1)=(x-1)(x+1), and some things will cancel out.
  4. Jan 17, 2009 #3


    User Avatar
    Homework Helper

    Note that x2-1=(x+1)(x-1)

    Use some indices and you should get it.
  5. Jan 17, 2009 #4
    The exact thing I needed!

    Thank you guys, I can't appreciate this enough.
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