1. **State the problem:** Solve for $t$ in the equation $$30 = 5 \times 1.2^t$$. 2. **Isolate the exponential term:** Divide both sides by 5 to get $$\frac{30}{5} = 1.2^t$$. 3. **Simplify the fraction:** $$\frac{\cancel{30}}{\cancel{5}} = 6 = 1.2^t$$. 4. **Use natural logarithms:** Take the natural logarithm of both sides to solve for $t$: $$\ln(6) = \ln(1.2^t)$$. 5. **Apply logarithm power rule:** $$\ln(6) = t \times \ln(1.2)$$. 6. **Solve for $t$:** $$t = \frac{\ln(6)}{\ln(1.2)}$$. 7. **Calculate the value:** Using approximate values, $$\ln(6) \approx 1.791759$$ and $$\ln(1.2) \approx 0.182322$$, so $$t \approx \frac{1.791759}{0.182322} \approx 9.82$$. **Final answer:** $$t \approx 9.82$$.