Can the solution for (1/3)^x = log<a>x be found without using a slider?

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I think this depends on the value of a.
 
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.
 
CP2016 said:
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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