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