Compute the time complexity of the following recurrence relation by applying Master

Theorem:

$($i$)$ T $($n$)=-.\mathrm{.}1$T

$($

$2$

$$

n

j$+$ log n

$($ii$)$ T $($n$)=$ T$(117)+$ log n

$($iii$)$ T $($n$)=2$T

$($

$1$

$+$ n$2$

$2$ logn

$($iv$)$ T $(12)=2$T$($

n $1+$

$2$ j n

$($n

$($v$)$ T $($n$)=$ T $+$ sin n