(Solved): please show steps! You have 5 algorithms, A1 took \( O(n) \) steps, A2 took \( \Theta(n \log n) \) ...

please show steps!

You have 5 algorithms, A1 took \( O(n) \) steps, A2 took \( \Theta(n \log n) \) steps, and A3 took \( \Omega n^{2} \) steps, A4 took \( o\left(n^{3}\right) \) steps, A5 took \( \omega\left(n^{3 / 2}\right) \) steps. You had been given the exact running time of each algorithm, but unfortunately you lost the record. In your messy desk you found the following formulas: (a) \( 4\left(5^{3 \log _{5} n}\right)+12 n+9527 \) (b) \( \sqrt[5]{3 n !} \) (c) \( \frac{5^{\log _{16} n^{2}}}{6}+4 n+17 \) (d) \( 3 n \log _{3} n+\left(\log _{2} n\right)^{3} \) (e) \( \log _{4} \log _{2} n+61 \) (f) \( 2^{5 \log _{4} n} \) (g) \( \left(\log _{2} n\right)^{2}+\log _{3} \log _{3} n \)