log-convex can be added, so log(exp(x^2) + exp(2*x^2)) is allowed.
log-concave can’t be added, so log(exp(-x^2) + exp(-2*x^2)) is not allowed.
Read the answer by mcg at Log of sigmoid function to learn the CVX rules for log-convex and log-concave. This material is not really addressed in the CVX Users’ Guide.