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