Linear and Logarithmic Constraint in Semidefinite Programming

Question

I am trying to minimize the largest component of a vector $x = [x_1, x_2, x_3, x_4]$, where $x_1 \ge x_2 ... \ge x_4$, such that it satisfies a set of linear inequalities $A, b$ in the following way:

$$ Ax \le b. $$

Furthermore, I want that, the Shannon entropy of the vector $x$ satisfies the following:

$$ -\sum_i x_i \log_2(x_i) = q, $$ for some constant $q$.

I can write the following for the first constraint:

cvx_begin sdp

variable x(4, 1) 

minimize x(1)
subject to 
    A * x <= b

cvx_end

However, when I try to include the second constraint, like: quantum_entr(diag(x)) == q.

I get the following error:

Invalid constraint: {concave} == {real constant}

Is there a way to mix these two types of constraints in a semi-definite program? Thanks!