Analyze the recurrence relation. Use substitution to establish its complexity

class, providing a step$-$by$-$step explanation.

$1.$ T$($n$)=2$T$($n$1)+1,$ with T$(1)=1$

$2.$ T$($n$)=$ T$($n$2)+$n$2,$ with T$(1)=1$ and T$(2)=2$

$3.$ T$($n$)=3$T$($n$5)+$n$,$ with T$(0)=0$

$4.$ T$($n$)=2$T$($n$1)+3$n$,$ with T$(1)=2$

$5.$ T$($n$)=$ T$($n$1)+$log$($n$),$ with T$(1)=0$