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Solve (1/3)^x = log<a>x

  1. Jun 12, 2016 #1
    1. I hit this logarithm mathematics problem.


    2. (1/3)^x = log<a>x
    For clarifications, <a> means the base a




    3. I have used GeoGeBra to graph them and managed to find the intersection.

    But is there a solution for the exact value(s) of x?
     
  2. jcsd
  3. Jun 12, 2016 #2

    Math_QED

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    I think this depends on the value of a.
     
  4. Jun 12, 2016 #3
    That is also what I have thought. I think the question is wrongly set because I was using the slider in GeoGebra without which I got no where to go.

    But I when tried putting a=3, just an arbitrary one, I could not figure out.
     
  5. Jun 12, 2016 #4

    Ray Vickson

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    The solution involves a non-elementary function, in this case the so-called Lambert W function; see, eg.,
    https://en.wikipedia.org/wiki/Lambert_W_function.
     
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