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Difficult Floor Function... Please help

  1. Aug 15, 2015 #1
    hi i'm new here. For a couple of days i am struggling to methodically solve an equation involving the integer part of a fraction but nothing yet. The equation is;
    I found that the apparent solution is 53 as x HAS to be integer. Yet, I cannot mathematically prove how to compute x to be equal to 53. Any opinion is welcome, thanks!

    Attached Files:

  2. jcsd
  3. Aug 15, 2015 #2


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    Staff: Mentor

    There is no way to solve the equation analytically with x and ln(x) like that. Numerical approaches are the best option, for small integer x this just means trial and error.

    52 to 56 all work for x.
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