Jensen's inequality with expectation of log and determinant

Question

I have a question when I try to have some analysis on the following expression. \begin{align} \mathbb{E}\left[\log_2\det\left(\mathbf{I}_L+\mathbf{X}\right)\right], \end{align} where $\mathbb{E}$ denotes the expectation, $\log_2$ denotes the log function based on 2, $\det$ denotes the determinant operation, $\mathbf{I}_L$ is a identity matrix of size $L\times L$, and $\mathbf{X}$ is a non-diagonal matrix of size $L\times L$. My question is can I have the following inequality based on Jensen's inequality? \begin{align} \mathbb{E}\left[\log_2\det\left(\mathbf{I}_L+\mathbf{X}\right)\right]\le\log_2\det\left(\mathbf{I}_L+\mathbb{E}\left[\mathbf{X}\right]\right) \end{align} I know it is true if there is no det operation, but no sure the case with det.