How to write log(1+Ax)? A are two constant

[Erling (Erling D.Andersen)]

It seems you use cvxquad. I doubt that is needed and it is better to use Mosek without cvxquad as described in the 2020 update on:

CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions

How to use CVXQUAD’s better performing and more reliable Pade Approximant instead of CVX’s unreliable Successive Approximation method: Update as of the release of CVX 2.2 in January 2020: Except for use of Quantum (Matrix) Entropy and Matrix Logarithm related functions addressed later in this post, none of the following, to include reformulation, is necessary if CVX 2.2 is used with Mosek 9.x or higher as solver, in which case CVX will utilize Mosek’s native exponential cone capability, thereby…