Solve the following recurrence equations using the characteristic

equation.

$($a$)T(n)=2T(\frac{n}{3})+lo{g}_{3}n,$ for $n>1,n$ a power of $3$

$T(1)=0$

$($b$)T(n)=10T(\frac{n}{5})+n^2,$ for $n>1,n$ a power of $5$

$T(1)=0$

$($c$)$

$nT(n)=(n-1)T(n-1)+3$ for $n>1$

$T(1)=1$

$($d$)$

$nT(n)=3(n-1)T(n-1)-2(n-2)T(n-2)+4^n$ for $n>1$

$T(0)=0$

$T(1)=0$

$($e$)$

$n{T}^2(n)=5(n-1)T^2(n-1)+n^2$ for $n>0$

$T(0)=6,$

Just $B$ please