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As in the title. Here are my attempts and the given function:

Given function: $y=\frac {\log_2{x}-3}{2x} $

Inverse function: $$ x= \frac {\log_2{y}-3}{2y} $$ $$2xy=\log_2{y}-3 $$ $$ 2^{2xy}=\frac y8 $$

At this step i'm stuck, and dont know what to do next

1qwertyyyy
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    Try using the Lambert function : https://en.m.wikipedia.org/wiki/Lambert_W_function – Tuvasbien Dec 27 '19 at 14:48
  • @almagest The second one,as written above – 1qwertyyyy Dec 27 '19 at 15:07
  • @almagest But ive never written something like that in my post – 1qwertyyyy Dec 27 '19 at 15:16
  • @almagest Oh yes, and the problem is to inverse that, i think it is necessary to a problem to write what we come from – 1qwertyyyy Dec 27 '19 at 15:22
  • @almagest It also replaces 2x with 2y: it comes from definition of inverting relations – 1qwertyyyy Dec 27 '19 at 15:29
  • @almagest https://en.wikipedia.org/wiki/Inverse_function Look at "Graph of the inverse" section – 1qwertyyyy Dec 27 '19 at 15:32
  • @almagest Yes you do, but function $x^2$ doesnt have inverse function, but it has inverse relation which is: $y^2=x$ – 1qwertyyyy Dec 27 '19 at 15:37
  • @almagest Just plug into desmos some random f and then replace x with y, and u will see that graph of this equation is reflected to line y=x – 1qwertyyyy Dec 27 '19 at 15:45
  • @1qwertyyyy I think it is bad practice to switch $x$ and $y$. It would be better to express the inverse function as $x=g(y)$. But leaving that aside Tuvasbien gave you the answer: use the Lambert W function. You cannot express the inverse in terms of elementary functions. You need Lambert W. – almagest Dec 27 '19 at 16:31
  • @almagest Ok,can u help me with that? – 1qwertyyyy Dec 27 '19 at 16:31

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