Give asymptotically tight upper and lower bounds for $T(n)$ in each of the following

recurrences. Justify your answers.

$($a$)T(n)=5T(\frac{n}{3})+nlgn.$

$($b$)T(n)=8T(\frac{n}{2})+n^3\sqrt[\phantom{2}]{?}n.$

$($c$)$ T$($n$)=$ T$($n$/2)+$T$($n$/4)+$T$($n$/8)+$n

$($d$)T(n)=T(n-1)+lgn.$