Olympiad Mathematics || A Nice Exponential Algebra Problem || Radical Equation

[@key_board_x]

y^(y√y) = (y√y)^(y) → let: a = y√y
y^(a) = a^(y)
Ln[y^(a)] = Ln[a^(y)]
a.Ln(y) = y.Ln(a)
a/y = Ln(a) / Ln(y) → recall: a = y√y
(y√y)/y = Ln(y√y) / Ln(y)
√y = [Ln(y) + Ln(√y)] / Ln(y)
√y = [Ln(y) + Ln{y}^(1/2)] / Ln(y)
√y = [Ln(y) + (1/2).Ln(y)] / Ln(y)
√y = (3/2).Ln(y) / Ln(y)
√y = 3/2
→ y = 9/4

[@MathswithChinwendu]

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