# Infinite Multiplication $$=$$ Infinite Addition

Algebra Level 5

$\small \sqrt{5\sqrt{5\sqrt{5\sqrt{5\sqrt{\cdots}}}}} = \sqrt{x^2 + \sqrt{4x^2 + \sqrt{16x^2 + \sqrt{64x^2 + \sqrt{\cdots}}}}}$

If $$x$$ is a positive number satisfying the equation above, find $$x$$.

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