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 \(p\).