Question on power, If 2x^2x^2x^2x... =4 Solve for x

Question

I've seen this random example, in which

can anyone give me clue how to solve for $ x $ here?

Answer 1

It's, unfortunately, not a particularly well-defined problem, as infinite power towers aren't always well defined. However, if we want to apply algebraic techniques anyhow, notice that we can write it as $$2x^{\left(2x^{2x^{2x\ldots}}\right)}=4$$ where the inner expression on the left is equal to four for a solution, giving $$2x^4=4$$ which is easier to solve.

Answer 2

$$ 2x^{2x^{2x^{..}}}=4 \longrightarrow 2x^4=4 $$ $$ x^4=2 $$

I think you can do the rest.