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Homework Help: Presumably simple logarithm equationt

  1. Feb 6, 2013 #1
    1. The problem statement, all variables and given/known data

    What value of x satisfies the equation:

    6 [itex]\cdot[/itex] e2x = 4x

    3. The attempt at a solution

    If I'm not mistaken, I can move the 6 to the superscripted part of e, resulting in:

    e12x = 4x

    And then I can take the natural log of both sides, resulting in:

    12x = ln(4x)

    Assuming I haven't made any mistakes, this is what I have so far and I'm stuck. This is for a practice test and I have the answer listed as:

    ln6 / (ln4 - 2)

    I'm just not sure how to get there.
  2. jcsd
  3. Feb 6, 2013 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    You are mistaken. You can't do that. E.g. 2*32 = 18 ≠ 34 = 81.

    Just start with taking the ln of both sides right from the beginning:

    ln(6*e2x) = ln(4x)

    The log of a product is the sum of the logs:

    ln6 + 2x = xln4

    Can you take it from here?
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