\( x > e^{\ln {4}} + \frac{\log _{111} {1024}}{\log _{12321}{1024}} + 2 \times \log _{9} {0.\overline{3}} \)

\( x < \log _{2} {512^{34}} + \frac{\log _{49} {25^{4096}} }{\log _{\sqrt{7}} {5}} - 4086 \times \log _{25}{5} \)

The solution to this inequality is \( x \in (m, n) \) (of course, \( n > m \)). Enter answer as \( n - m \)

**Details**

\( 0.\overline{3} = 0.33333.... \)

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