this is what is on the book for solving it but i don't know how to do it$.$

$4-3$ Solving recurrences with a change of variables

Sometimes, a little algebraic manipulation can make an unknown recurrence similar to one you have seen before. Let$$s solve the recurrence

T $.$n$/$ D $2$T $$p

n

$$

C $.$lg n$/(4\mathrm{.}25)$

by using the change$-$of$-$variables method.

a$.$ De$$ne m D lg n and S$.$m$/$ D T $\mathrm{.}2$m$/.$ Rewrite recurrence $(4\mathrm{.}25)$ in terms of m

and S$.$m$/.$

b$.$ Solve your recurrence for S$.$m$/.$

c$.$ Use your solution for S$.$m$/$ to conclude that T $.$n$/$ D $.$lg n lg lg n$/.$

d$.$ Sketch the recursion tree for recurrence $(4\mathrm{.}25),$ and use it to explain intuitively

why the solution is T $.$n$/$ D $.$lg n lg lg n$/.$

Solve the following recurrences by changing variables:

Problems for Chapter $4121$

e$.$ T $.$n$/$ D $2$T $.$p

n$/$ C $\mathrm{.}1/.$

f$.$ T $.$n$/$ D $3$T $.$p$3$ n$/$ C $.$n$/.$