# 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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