Series Demystified 6

Algebra Level 4

$\large \sum_{n=1}^{48} \log \left ( \frac {n}{n^2+3n+2} \right )$

If the summation above equals to $$S$$, then $$S+\log(49!)=-\log P.$$ Find the value of $$P$$.

This is one of my original Series Demystified problems.
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