# Logging Domains

Algebra Level 4

The domain of the function $$y = \underbrace{\log_{10}{\log_{10}{\log_{10}{\ldots \log_{10}{x}}}}}_{786 \text{ times}}$$ could be represented as $$(\large 10^{10^{10^{10^{\cdot^{\cdot^{\cdot^{\text{p times}}}}}}}} , \infty)$$. Then find the value of $$p$$.

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