we can do this question by one more way.
T(n)=2T(⌈√n⌉)+1T(1)=1
Here, if a recursion program would be formed from this relation then, returning statement would be
return √n+√n +c( any other constant) which becomes 2T(√n) + c
for example, if we take n=8 then √8=2√2 whose ceiling value is 3 and ceiling value is also mentioned in the question.
and log8 base 2 =3
therefore Θ(log n)