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Solving logarithm equation help?

  1. Mar 24, 2009 #1
    1. The problem statement, all variables and given/known data

    log2(x+2)=log2x2

    -log base 2(X+2)= log base 2 (x2)

    3. The attempt at a solution

    I know the answer is supposed to be -1 and 2, but I get the wrong answer every time I try.
    I tried bringing log2x2 over to the other side and then got log2(2/x) which got me nowhere!

    What am I supposed to do to solve this? Any tips would be greatly appreciated :)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 24, 2009 #2
    There is a technique called exponentiation (I think) used to solve these types of equations. Just put both sides of the equation in an exponent that is the same as the logarithm base, like this:
    [tex]2^{log_{2} (x+2)} =2^{log_{2} (x^2}}[/tex]
    Then you can use the rules for logs an exponents to get to
    x+2 = x^2
     
  4. Mar 24, 2009 #3
    Right, it is called exponentiation. You can also see that both sides are ultimately a value within the log function. If the log base 2 of both sides is the same, then both sides must be the same. There is another step though that many people forget. When you exponentiate, you may get answers which do not work because on of the log functions is undefined for that value of x. You have to check each value you find for x to make sure that both log functions are defined for that value of x. If you do this particular problem right, both solutions work.
     
  5. Mar 24, 2009 #4
    Exponentiation isn't even necessary in this case. log is 1-1, so equality can only hold if the arguments are equal.
     
  6. Mar 24, 2009 #5
    Well, yes, it's still exponentiating, you're just skipping the steps in between.
     
  7. Mar 25, 2009 #6
    log2(x+2)=log2x2

    It's quite easy. The logarithms have the same base. Thus you can just work with it.

    (x+2) = x2

    Now, set the variable to 0 and factor
    x2-x-2 = 0
    (x-1)(x+2) = 0

    two answers are: x -1 = 0; x=1 or x+2=0; x=-2

    :)
     
  8. Mar 25, 2009 #7
    thanks everyone! this really helped :) Turned out I completely forgot about factoring...
     
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