My goal is to express \log(1+\frac {k_{20}}{(d_{20}+d_{21}x+d_{22}y)}), where k_{20},d_{20}, d_{21}, d_{22} are constant vectors (101x1), x,y are variables (101x1). \frac {k_{20}}{(d_{20}+d_{21}x+d_{22}y)} is positive.

Please show a reproducible example. If you can do it with smaller arrays, for example 3 by 1 instead of 100 by 1, that would be preferred. Please include the output from cvx_version.

rel_entr Scalar relative entropy.
rel_entr(X,Y) returns an array of the same size as X+Y with the
relative entropy function applied to each element:
{ X.*LOG(X./Y) if X > 0 & Y > 0,
rel_entr(X,Y) = { 0 if X == 0 & Y >= 0,
{ +Inf otherwise.
X and Y must either be the same size, or one must be a scalar. If X and
Y are vectors, then SUM(rel_entr(X,Y)) returns their relative entropy.
If they are PDFs (that is, if X>=0, Y>=0, SUM(X)==1, SUM(Y)==1) then
this is equal to their Kullback-Liebler divergence SUM(KL_DIV(X,Y)).
-SUM(rel_entr(X,1)) returns the entropy of X.

Disciplined convex programming information:
rel_entr(X,Y) is convex in both X and Y, nonmonotonic in X, and
nonincreasing in Y. Thus when used in CVX expressions, X must be
real and affine and Y must be concave. The use of rel_entr(X,Y) in
an objective or constraint will effectively constrain both X and Y
to be nonnegative, hence there is no need to add additional
constraints X >= 0 or Y >= 0 to enforce this.