1. **State the problem:** Solve the equation $$-6\log x - 5n + 3 = -21$$ for the variable $n$ assuming $\log$ is the logarithm function and $x$ is a constant or known value. 2. **Rewrite the equation:** $$-6\log x - 5n + 3 = -21$$ 3. **Isolate the term with $n$:** Subtract 3 from both sides: $$-6\log x - 5n = -21 - 3$$ $$-6\log x - 5n = -24$$ 4. **Move $-6\log x$ to the right side:** $$-5n = -24 + 6\log x$$ 5. **Solve for $n$ by dividing both sides by $-5$:** $$n = \frac{-24 + 6\log x}{-5} = \frac{24 - 6\log x}{5}$$ 6. **Final answer:** $$\boxed{n = \frac{24 - 6\log x}{5}}$$ This expresses $n$ in terms of $\log x$. If $x$ is known, substitute its value to find $n$.