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$\large \color{#D61F06}{\sqrt{\log_2(2x^2) \times \log_4(16x)}=\log_4x^3}$

If $a_1,a_2,...a_n$ are all the real roots of the above equation, then find the value of $\dfrac{a_1+a_2+...+a_n}{n}$

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