# What does this bar notation mean?

I have a problem in which I need to solve for $$x$$ in the question (in image) below, but I don't even understand it. Is this suppose to be a matrix? $$\begin{vmatrix}\ln(2x+1)&2-\ln x\\1&1\end{vmatrix}=0$$

• I think a picture or rendering it in LaTeX would prove more useful, because the bit you pasted renders as nonsense for me. – Eevee Trainer Nov 29 '20 at 9:26
• @EeveeTrainer I've added a picture! – Mya Ishikawa Nov 29 '20 at 9:30
• This looks like the determinant of a $2 \times 2$ matrix by my eye. – Eevee Trainer Nov 29 '20 at 9:32

The bar notation means taking the determinant of the matrix enclosed. This is a shorthand for $$\det M$$.
The bar notation is used to indicate the determinant of a matrix. It converts a matrix into a scalar. For example, \begin{align}\begin{vmatrix} a & b\\c & d \end{vmatrix}=ad - bc \end{align} Other common notations are $$\det A$$ and $$\det (A)$$.
In particular, for your case, the mentioned determinant becomes \begin{align}\begin{vmatrix} \ln (2x+1) & 2-\ln x\\1 & 1 \end{vmatrix}=\ln (2x+1)-2+\ln x = \ln (2x^2+x)-2 \end{align}