how to solve discrete logarithm problem information requested
Let $f(x,y) = -y^2 + x^3+17230x+22699$ over $\Bbb F_p$ with $p=23981$. A point on the curve is a singular point if and only if the partial derivatives are vanishes at that point. The partial derivatives are;


$\frac{\partial f}{\partial x} = 3x^2 + 17230 =0 \pmod p$ and vanishes at $x=\{185,23796\}$ found by WolframAlpha or it can be found by Tonelli-Shanks.
$\frac{\partial f}{\partial y} = -2y = 0 \pmod p$ and vanishes at $y=0$ 


The vanishing point $(185,0)$ is not on the curve, however, $(23796,0)$ is.

Therefore $(23796,0)$ is a singular point for the Curve.

Then we then translate the origin to this singular point $(23796,0)$, that is replace $(x,y)$ by $(x+23796,y+0$) in the equation of $E$, yielding the equation of the curve in the shifted referential:
$$y^2 = x^3 + 23426x^2$$
The rest is in the answer which the OP had trouble with.

Note: credit goes to @kelalaka for the better of the present answer, in particular introducing $f(x,y)$ and its partial derivatives.