Let the tangent at any point P on a curve passing through the points (1,1) and (1/10, 100), intersect positive x -axis and y -axis at the points A…

Let the tangent at any point P on a curve passing through the points $\displaystyle (1,1)$ and $\displaystyle \left(\frac{1}{10}, 100\right)$, intersect positive $\displaystyle x$-axis and $\displaystyle y$-axis at the points A and B respectively. If $\displaystyle \mathrm{PA}: \mathrm{PB}=1: k$ and $\displaystyle y=y(x)$ is the solution of the differential equation $\displaystyle e^{\frac{d y}{d x}}=k x+\frac{k}{2}, \mathrm{y}(0)=k$, then $\displaystyle 4 y(1)-5 \log _{\mathrm{e}} 3$ is equal to $\displaystyle \_\_\_\_$.