log base anything of 1, is 0.
so
n^((1/2)^k) = 1
log(n)(n^((1/2)^k)) = log(n)(1)
1/2^k = 0
log(1/2)((1/2)^k) = log(1/2)(0)
log base anything of 0 is negative infinity.. so...
k = -infinity.
I think you should use a different "final number" for n, than 1
just saying...