What is this kind of numerical method called and what is the intuition behind it?

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To solve for x in the equation : 2^x=x^3,

$2^x=x^3$
establish x=f(x) which is
$x=2^{x/3}$ and iterate
$x_{n+1}=2^{x_{n}/3}$

What is this kind of numerical method called and what is the intuition behind it?