Can you solve these logarithmic equations?

Algebra Level 4

log2a+log4b+log4c= 2log3b+log9c+log9a= 2log4c+log16a+log16b= 2\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 aa, bb and cc satisfy the above system of equations, find the value of 6a+8b3c6a+8b-3c.

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