Real Analysis: continuity

Sorry, only a few more, lasts ones I'm not sure of, final on Friday, these are some of the review problems I don't get:

1) Show 2^x = 3x for some xE (0,1)

2) let f(x) = { x xrational

0 xirrational

a. prove lim f(x) = 0

x->0

b) Prove that lim f(x), does not exist for c not equal to 0.

x--> c

3) Suppose f is uniformly continuous on [a,b] and uniformly continuous on [b,c] Prove using an epsilon-delta argument that f is uniformly continuous on [a,c]

Thanks, this professor does a horrible job at teaching, and I'm really lost, any help, even how to start any of these would be great, thanks!