Exponential inequality!

Algebra Level 2

\[4(9^ x)-19(3^ x)+12\leq 0\]

For the above inequality to be true, \( x\in \left[ \log _{ b }{ a } , \log _{ b}{ c } \right] \), where \(a,b\) and \(c\) are positive integers, find the minimum value of \(a\)+\(b\)+\(c\).

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