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For parameters $a$ and $b$, both of which are $\omega(1)$, $T(n) = T(n^{1/a})+1$, and $T(b)=1$. Then $T(n)$ is

  1. $\Theta (\log_a  \log _b  n)$   
  2. $\Theta (\log_{ab} n$)
  3. $\Theta (\log_{b}  \log_{a}  \: n$)
  4. $\Theta (\log_{2} \log_{2} n$)
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