How to use log2(det(.)), log10(det(.)) inside the cvx?

How to use log2(det(.)), log10(det(.)) in the objective inside the cvx_begin quiet? Is it same as log_det(.)?

Here I am not getting how to write above equations inside the cvx_begin quiet? Above equations are used in the objective to maximize the weighted sum-rate, such that only Q_c and X_k are variables, where authors used SCA (successive convex approximation)

log10(det(X)) = log_det(X)/log(10)
log2(det(X)) = log_det(X)/log(2)