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Homework Help: Log equation question

  1. Jan 14, 2009 #1
    1. The problem statement, all variables and given/known data
    Solve for x:
    2log3x + log3(x-1) = log32 + log36x

    2. Relevant equations
    N/A


    3. The attempt at a solution
    Ok, so I tried to solve it and I came up with this and got stuck.

    log3(x3-x2) = log312x
    Even if I cancelled out the logs it would be x3-x2 = 12x and then how would I solve?
     
    Last edited: Jan 14, 2009
  2. jcsd
  3. Jan 14, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi chops369! Welcome to PF! :smile:
    Divide both sides by x. :wink:
     
  4. Jan 14, 2009 #3
    Ohhhh, I see now. I didn't know you had to factor. Thanks a lot.
     
  5. Jan 15, 2009 #4
    Careful of dividing by x! It's OK in this problem since x=0 is an extraneous solution, but you do run the risk of losing a solution.
     
  6. Jan 16, 2009 #5
    It is better if you factor x:
    x3-x2-12x=0

    x(x2-x-12)=0

    One of the solutions is x1=0

    The other two come from the quadratic equation.

    As you can see zero, can't be solution because if you put the 0 in the first equation, it would not be possible since log30 doesn't exist.

    Regards.
     
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