If the domain of the function \(\ln(\ln(\ln(\ln(\ln(x)))))\) is \((a,\infty)\), solve for \(a\).
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**Note**:

\(e \) is a mathematical constant which approximates to \(2.71828 \).

We denote the tetration notation: \(^n e = \underbrace{e^{e^{e^{.^{.^{.^e}}}}}}_{n \text{ number of times}} \)

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