construct an "inverse" fn of lg*, := 2^^n, means 2^2^2^2....^2 (# of 2 is n);
so for 2^^(n-1)<x<=2^^(n), we have lg* (x)=n+1
lhs=lg*(lg(x)), lhs=n
rhs=lg(lg*(x)), rhs=lg(n+1)
at last solve this transcendental eq: n=lg(n+1)
we get n=1, i.e. x=2 is the symmetric point
x>2, lhs>rhs
x<=2, =