1. **State the problem:** Solve the logarithmic equation $$\log(5x^2) - \log(8) = 1$$. 2. **Recall the logarithm subtraction rule:** $$\log(a) - \log(b) = \log\left(\frac{a}{b}\right)$$. 3. **Apply the rule:** $$\log\left(\frac{5x^2}{8}\right) = 1$$ 4. **Rewrite the logarithmic equation in exponential form:** Since the base of the logarithm is 10 (common log), $$\frac{5x^2}{8} = 10^1 = 10$$ 5. **Solve for $x^2$:** $$5x^2 = 8 \times 10 = 80$$ 6. **Divide both sides by 5:** $$x^2 = \frac{80}{5}$$ 7. **Show cancellation:** $$x^2 = \frac{\cancel{80}}{\cancel{5}} = 16$$ 8. **Take the square root of both sides:** $$x = \pm \sqrt{16} = \pm 4$$ 9. **Check for extraneous solutions:** Since $\log(5x^2)$ requires $5x^2 > 0$, both $x=4$ and $x=-4$ are valid. **Final answer:** $$x = \pm 4$$