# can't quit understand one step of the recurrence time complexity calculation

I solved the question T(n) = T(sqrt(n)) + 1 but can't quit understand one step of the solution

I don't understand the transition in (1). how did we conclude that T(m) = T(m/2) + 1 from the previous step that m is in the power?

It obviously is not correct. To fix it, define $$S(m)=T(2^m)$$, and then we would have $$S(m)=S(m/2)+1$$. Now, continue with the proof replacing everywhere $$T(m)$$ with $$S(m)$$. After you solve what $$S(m)$$ is, substitute $$m=\log(n)$$ in the solution to get what $$T(n)=T(2^m)=S(m)$$ is.