Solve for x in (4/2x) = 8^(2x)?
The way you typed it:
(4/2x) = 8^(2x)
2x = 8^(2x)
2x = (2^3)^(2x)
2x = 2^(6x)
x = 2^(6x-1)
at this point, you will have to use some type of
calculator-based method, such as Newtons Method
let's graph it to see what it looks like.
https://www.wolframalpha.com/input/?i=plot+y+%3D+x,+y+%3D+2%5E(6x-1)
Ahhh, from the graph we can see there is no real solution.
Check your typing. You must have a typo, perhaps you mean something like
4^(2x) = 8^(2x)
In that case x = 0 is the only solution
https://www.wolframalpha.com/input/?i=plot+y+%3D+4%5E(2x),+y+%3D+8%5E(2x)+from+-1+to+0.1