Whats my real age?

Calculus Level 5

Like many who use brilliant, I faked my age. For those who know me, this is a give away. Seriously, a give away:

What is the minimum value of AA if AA is a positive (obviously) integer?

g=2.218654762loggloggloggAgggg=2.218654762\\ \\ \log _{ g }{ \frac { \log _{ g }{ \frac { \log _{ g }{ \frac { A }{ g } } }{ g } } }{ g } }

This question was inspired by the boredom of Geography, therefore the log constant is g.

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