Using CVXQuad' pade approximant

I have for example a function like this after putting it in a form of a difference of two convex,
log(1 + 1/x) - log(1 + 1/x^2)
and after some approximations I converted the first log into a concave form to be an overall concave function.

I have used the conversion mentioned on MOSEK site for (1/x^2), such that
exp(t2) replaces (1/x^2)
so the overall function is still also a concave.

If I would like to replace successive approximation with Pade approximation, I will need to replace
“log(1 + 1/x^2)” with “-rel_entr(1,1+exp(t2))”
“exp(t2)” with “z”
so the expression becomes “-rel_entr(1,1+z)” which is concave, not convex, causing an error in solving the problem “{concave}-{concave}”

Any suggestion?
Thank you,

Handle log(1 + 1/x^2)<=Q like
log_sum_exp( [0,t2] )<=Q;