a$)$ Design a Turing Machine to accept $|)$:$\}$ is in $\{$:$(a+b{)}^{**}\}$

b$)$ Construct Turing Machine to compute the function $lo{g}_2^n$

c$)$ Design a TM to recognize the language $L=\{1^n{2}^n{3}^n|n1\}$

d$)$ Design TM which will recognize strings containing equal number of a$\text{'}$s and b$\text{'}$s

e$)$ Design a $TM$ to recognize the language $L=\{0^n{1}^n{0}^n|n1\}$