1. **State the problem:** Solve the equation $$2 = 3^{0.01t}$$ for $t$. 2. **Recall the formula and rules:** To solve for $t$ when it is in the exponent, use logarithms. The key property is: $$a^x = b \implies x = \log_a b$$ 3. **Apply logarithm to both sides:** $$\log_3 2 = \log_3 3^{0.01t}$$ 4. **Use the logarithm power rule:** $$\log_3 3^{0.01t} = 0.01t \cdot \log_3 3 = 0.01t \cdot 1 = 0.01t$$ 5. **Set up the equation:** $$\log_3 2 = 0.01t$$ 6. **Solve for $t$:** $$t = \frac{\log_3 2}{0.01}$$ 7. **Convert to natural logarithm (optional):** $$t = \frac{\frac{\ln 2}{\ln 3}}{0.01} = \frac{\ln 2}{0.01 \ln 3}$$ 8. **Calculate approximate value:** $$\ln 2 \approx 0.6931, \quad \ln 3 \approx 1.0986$$ $$t \approx \frac{0.6931}{0.01 \times 1.0986} = \frac{0.6931}{0.010986} \approx 63.1$$ **Final answer:** $$t \approx 63.1$$