# Weird exponent

Level pending

The value of $$x$$ that satisfies the equation

$$8^{x^{x^{x^\cdots}}}=4$$

can be expressed as $$\frac{a\sqrt{b}}{c}$$ where $$a,b,$$ and $$c$$ are positive integers, $$a$$ and $$c$$ are relatively prime, and $$b$$ is not the square of any prime. Find $$abc$$.

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