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$\large\begin{aligned}\begin{aligned}\log_2a+\log_4b+\log_4c=&\ 2\\\log_3b+\log_9c+\log_9a=&\ 2\\\log_4c+\log_{16}a+\log_{16}b=&\ 2\end{aligned}\end{aligned}$

If $a$, $b$ and $c$ satisfy the above system of equations, find the value of $6a+8b-3c$.

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