Logarithmic Function Behaivour

Question

I have read about Logarithmic function. We can use the second-order condition to show that the $f(x)=\log_2(1+x), x \geq 0$ is a concave function. Now, is $g(x)$ a concave function? How can I prove this fact? \begin{equation} g(x)=(1-\frac{x}{a})\sum_{k=1}^K \log_2(1+\frac{b_kx}{-c_kx^2+d_kx+e_k}), \quad x \in [0,a] , \quad a>1 , \quad \forall k \in\{1,\ldots,K\}, \quad b_k,c_k,d_k,e_k>0 \end{equation} where $a,b_k,c_k,d_k,e_k$ are positive constants and $d_k$ , $e_k$ for all $k$ are enough large so that $-c_kx^2d_kx+e_k>0$.