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A simple logarithmic equation

  1. Feb 10, 2010 #1
    Can anyone please tell me what is wrong with this solution

    log(5x-17) = log(4x-14)
    As logarithmic functions are one-one so,
    5x-17 = 4x-14
    => x =3
  2. jcsd
  3. Feb 10, 2010 #2


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    Science Advisor

    That's a very good question Ali. The problem is the domain of the log function over the reals.

    So there is no solution over the domain of real numbers, however x=3 is a solution if the domain is the complex number field. This is an interesting result in the sense that we require the existance of complex numbers in order for a solution to exist, even though the solution itself is not complex!
  4. Feb 10, 2010 #3
    What's basically wrong is that neither of the logarithms (in their real sense) are defined for x=3 since their argument will be negative. Comes in what uart said.
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