Can you solve these logarithmic equations?

Algebra Level 4

\[\large\begin{eqnarray}\begin{split}\log_2a+\log_4b+\log_4c=&\ 2\\\log_3b+\log_9c+\log_9a=&\ 2\\\log_4c+\log_{16}a+\log_{16}b=&\ 2\end{split}\end{eqnarray}\]

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

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