Use
log2(x) = log(x)/log(2)
to re-write log2 in terms of log
Use the relation
X*log(1+y/x) = -rel_entr(x,x+y)
to reformulate R1 and R2 in terms of rel_entr.
I recommend you install CVXQUAD to solve it more reliably. 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