my first problem is to rewrite |x-2|+|3-x| given that 0<x<2

What I've done so far is that given the values possible for x, the x-2 portion is negative making it:

(-x+2)

with the same reasoning the 3-x portion is always positive keeping it as is so I come up with:

(-x+2)+(3-x)

and once I simplify I get 5-2x, is this correct or did I do a step wrong?

the second problem I have is rewriting ln(sqrt(e)) = 1/2 to exponential form

What I did here was rewrite the sqrt(e) to e^1/2, then bring down the 1/2 via the ln(a^b) = b ln (a) rule and I'm stuck at

1/2 ln(e) = 1/2

I'm not sure what I do now to get it to exponential form, the ln and sqrt e get me confused, any help on what I'm supposed to do?

Thanks