Differential Equations: JEE Main 2023 Mathematics question

Let the tangent at any point P on a curve passing through the points (1, 1) and $\left(\frac{1}{10}, 100\right)$, intersect positive $x$-axis and $y$-axis at the points A and B respectively. If $\mathrm{PA}: \mathrm{PB}=1: k$ and $y=y(x)$ is the solution of the differential equation $e^{\frac{d y}{d x}}=k x+\frac{k}{2}, y(0)=k$, then $4 y(1)-6 \log _{\mathrm{e}} 3$ is equal to ____________.