1. **State the problem:** Solve the equation $a x^2 - x y = 3 f \ln x$ for one of the variables or simplify it. 2. **Understand the equation:** The equation is $a x^2 - x y = 3 f \ln x$ where $a$, $f$ are constants, and $x$, $y$ are variables. 3. **Isolate $y$:** To express $y$ in terms of $x$, rearrange the equation: $$a x^2 - x y = 3 f \ln x$$ Subtract $a x^2$ from both sides: $$- x y = 3 f \ln x - a x^2$$ Divide both sides by $-x$ (assuming $x \neq 0$): $$y = \frac{a x^2 - 3 f \ln x}{x}$$ 4. **Simplify the expression:** Divide each term in the numerator by $x$: $$y = a x - \frac{3 f \ln x}{x}$$ 5. **Interpretation:** This expresses $y$ as a function of $x$, constants $a$ and $f$, and the natural logarithm of $x$. **Final answer:** $$y = a x - \frac{3 f \ln x}{x}$$