Reverse Logarithmic Inequality

Algebra Level 3

1log4(x+1x+2)<1log4(x+3) \dfrac{1}{\log_{4}\left(\dfrac{x+1}{x+2}\right)}<\dfrac{1}{\log_{4}(x+3)}

If the range of xx that satisfy the equality above is (a,)(a,\infty), find the value of aa.

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