$5.$ Give asymptotic bounds for T$($n$)$ in each of the following recurrences. Assume that T$($n$)$ is

constant for n $<=2.$ Make your bounds as tight as possible, and justify your answers.

$($a$)$ T$($n$)=8$T$($n$/2)+$ n

$3$

n

$($b$)$ T$($n$)=$ T$($n $1)+$ log n

$($c$)$ T$($n$)=3$T$($n$/27)+$ n

$0\mathrm{.}25$

$($d$)$ T$($n$)=16$T$($n$/4)+$ n

$2$

log$2$ n