On unravelling exponential formulas
According to St. Petersburg Academy records, it was presented to that Academy on June 12, 1777.
The problem Euler addresses in this paper was posed by Condorcet. Euler takes r positive and α real, then asks for what values the sequence r, r α, r r α, r r r α, ... converges. The critical value seems to be at r = e1/e ≈ 1.44467.
Original Source Citation
Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 1777: I, pp. 38-60.
Opera Omnia Citation
Series 1, Volume 15, pp.268-297.