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Homework Help: Solving log equations

  1. Nov 11, 2007 #1
    1. The problem statement, all variables and given/known data
    Solve the equation
    log base 7 (7x+8) = log base 7 (7x+3)

    2. Relevant equations

    I don't think you use equations for this, just the properties of logarithms

    3. The attempt at a solution

    I thought since they have the same base you could set the parts in parenthesis equal to each other

    (7x+8) = (7x+3)

    so you get
    8=3 or

    but that can't be right...
  2. jcsd
  3. Nov 11, 2007 #2


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    Well that should be correct.....but if you knew what the graphs looked like, you would see that they are just horizontal shifts of each other...so it is kind of like they are "parallel' or so to say...meaning that they do not intersect
  4. Nov 11, 2007 #3
    so that means there is no answer?
  5. Nov 11, 2007 #4


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  6. Nov 11, 2007 #5


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    You correctly remarked that if the expressions on both sides of the equation use the same base for the logarithm, then the arguments of the log functions on each side must be equal. So, if you typed this correctly, that would be asking for the value of x such that 7x + 8 = 7x + 3 . You also observed that there is no such value possible. So that is your answer: there is no solution to this equation. (That can happen occasionally in a homework or exam problem, or in Real Life. Demonstrating that a solution doesn't exist can be just as meaningful as finding a solution...)
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