Give asymptotically tight upper and lower bounds for T$($n$)$

in each of the following recurrences. Justify your answers.Give asymptotically tight upper and lower bounds for T$($n$)$

in each of the following recurrences. Justify your answers.

a$.$ T$($n$)=4$T$($n$/3)+($nlog$34)$log$3$n

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

Hint: Consider a change of variable, as discussed in the book on Page $120$ Problem $4-3$

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