For what value of $x$ is this matrix invertible? I've been given the following matrix $X$:
$$X=
\begin{bmatrix}
1 & 4 & 8 & 1 \\     
0 & 30 &1  &  0 \\    
0 &2&  0&  0 \\     
1 &2 & 9 & x \\
\end{bmatrix}
$$
and I have to determine for which value of $x$ the matrix is invertible.
Any hints/suggestions would be greatly appreciated.
So far I have substituted different values for $x$, but there seems to be an inverse for all values of $x$ above $1$.

Hint: You may use the well-known relation:
$$
\operatorname{tr}(X) = \log\Big(\det\big(\exp(X)\big)\Big)
$$
