Tens Everywhere

Algebra Level 5

\[\large \frac{1}{10} \log _{\frac{x}{10} } 10 > 10 \log _{10} \left(\frac{x}{10} \right) \]

What is the sum of all positive integers that satisfy the above inequality?

Submit your answer as 999 if you think that there are infinitely many positive integers that satisfy the inequality.

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