If $$2^{2^{x^2-1}}=16$$, then the value of $$x^4$$ is

Correct Answer: 9

Since $$16=2^4$$,

$$2^{2^{x^2-1}}=2^4$$

equating the powers we get $$2^{x^2-1}=4=2^2$$.

Equating the powers once again we get $$x^2-1=2$$, so $$x^2=3$$ and therefore $$x^4=9$$.

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