How to code 1/log in geometric programming in cvx?

I am trying to solve the given joint optimization problem:

minimize \frac{1}{\bar R}+\sum\limits_{i=1}^{N} \frac{1}{R_i} + \left(\frac{1}{\sum\limits_{i=1}^{N}t_{i}\prod\limits_{k \neq i}^{N}(1-t_k)}-1 \right)

where R_i = log_{2}(1+P_{i}) and \bar R = min(R_i) \forall i.

The variables of optimization are P and t. The problem is a convex optimization problem.

The part i.e.\left(\frac{1}{\sum\limits_{i=1}^{N}t_{i}\prod\limits_{k \neq i}^{N}(1-t_k)}-1 \right) of the problem requires gp to solve, however, gp gives error when I try to code R since it is a logarithmic function of P.

That is not a valid GP.

Here are the rules for disciplined GP.

Can I solve it using cvx by applying any kind of transformation? To add, I am able to solve the function of t using GP. The only problem is with the function of P.