1. **Problem statement:** Solve for $x$ in the equation $\log_2 (x - 1) = 3$. 2. **Formula and rules:** Recall that $\log_a b = c$ means $a^c = b$. 3. **Apply the formula:** From $\log_2 (x - 1) = 3$, we get $$2^3 = x - 1$$ 4. **Calculate the power:** $$8 = x - 1$$ 5. **Solve for $x$:** $$x = 8 + 1 = 9$$ 6. **Check domain:** Since the argument of the logarithm must be positive, $x - 1 > 0 \Rightarrow x > 1$. Our solution $x=9$ satisfies this. **Final answer:** $$x = 9$$