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

  • #1
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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?
 

Answers and Replies

  • #2
Math_QED
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I think this depends on the value of a.
 
  • #3
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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.
 
  • #4
Ray Vickson
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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.
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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