Please state clearly and carefully what your question is.
Do you wish to include the constraint
t*lnt/(1-t)-ln(0.1)<0
?
If so, what is Int?
if t is a convex expression, as in your code, and not a variable (or affine expression) , that could be very relevant.
Once you clearly write out the constraint you want, taking careful account of what the variables and various types of expressions are, then you should prove the convexity of your constraint.