a,b are all positive variables,can this constraint be expressed in CVX?

Unlike your previous constraint at Constraint:a*log(1+b/a)>c

if a and b are separate variables, the LHS is neither concave nor convex. Therefore the constraint s non-convex.

my idea is convert this expression to :
a*log(1+c/a)>k,c=a/b ,
then use rel_entr

That is an attempt at convex alchemy. c = a/b is not convex.

If that is the constraint you need, then use a tool such as YALMIP which can accept and attempt to solve non-convex problems