Poland | A Very Nice Exponential Algebraic Problem | Exponential Math | Find X??

A Very Nice Exponential Algebraic Problem | Exponential Math | Find X??
Nice square root math simplification | Math Olympiad | Find X
Nice Olympiad Math problem
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[p.g.]

Nice one. You can do it much faster though. If you have the step 4^4 = x^(256/x) Then this is already the solution because of: 4^4=256. --> 256 = x^(256/x) --> 256 ^(256/256) = x^(256/x) then you instantly have x = 256.

[jimmpenn]

What did I miss? How did we go from 4^(1/64) ---> 4^((2/2)*64)?

[leoperellis]

Why doesn’t Geogebra show this solution?
(Alright, I just figured out the size immensity of the terms)

[marcelopacheco]

x^y=(x^2)^(y/2) with this easily verifyable identity we can solve in many fewer steps.
4^x=x^64
16^(x/2)=x^64
256^(x/4)=x^64
if 256=x then test x/4=64 true
so x=256