Solve all the following recurrences using the Master Method $($if possible$)$ and the first five of them using the recursion tree method.

Each of the five recursion tree solutions is worth $12$ points, and each of the eight Master Theorem solutions is worth $5$ points. To get full credit, you must show all steps. You will lose points for any missing steps, especially on the recursion tree problems.

$1.$

$2.$

$3.$

$4.$

$5.$

$6.$

$7.$

$8.$