1. **State the problem:** Simplify the expression $$-1 \times \ln\left(\frac{s^2 - 2}{\sqrt[3]{s^2 + 2}}\right)$$. 2. **Recall logarithm properties:** For any positive $a,b$ and real $x$, - $\ln\left(\frac{a}{b}\right) = \ln(a) - \ln(b)$ - $x \ln(a) = \ln(a^x)$ 3. **Apply the logarithm quotient rule:** $$-1 \times \ln\left(\frac{s^2 - 2}{\sqrt[3]{s^2 + 2}}\right) = -1 \times \left(\ln(s^2 - 2) - \ln\left((s^2 + 2)^{\frac{1}{3}}\right)\right)$$ 4. **Distribute the $-1$:** $$= -\ln(s^2 - 2) + \ln\left((s^2 + 2)^{\frac{1}{3}}\right)$$ 5. **Use the power rule of logarithms:** $$\ln\left((s^2 + 2)^{\frac{1}{3}}\right) = \frac{1}{3} \ln(s^2 + 2)$$ 6. **Final simplified expression:** $$\boxed{\frac{1}{3} \ln(s^2 + 2) - \ln(s^2 - 2)}$$ This is the simplified form of the original expression using logarithm properties.