An algebra problem by Florin Celoiu

Algebra Level 3

\[\Large n^{5^{ (\log_{5}2) + (\log_{5}x )+ \log_{5}\left(1-\frac{9}{2x}\right) }}=n^{7^{(\log_{7}56) - \log_{7}x}}\]

For \( n \geqslant 2 \), what is the positive integral value of \( x \) which satisfies the above equation?

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