log3(x^log3(x)) = 9

Question

How do you solve for x?

Answer 1

x^log3(x) = 3^9

log3 (x^log3(x)
= log3(x) log3(x) = 3^9

log3 (x) = 3^(9/2) = 3^4.5 = 140.3

3^log3(x) = x = 3^140.3
check my arithmetic, did quickly