# Logs are cool

Algebra Level 3

Solve
$\large \log_{2x+3}(6x^{2}+23x+21) = 4-\log_{3x+7} (4x^{2}+12x+9)$

Let the only solution. of $$x$$ in the above equation be represented as $$-\dfrac{m}{n}$$, where $$m$$ and $$n$$ are coprime positive integers. Find $$m+n$$.

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