1. **State the problem:** Solve the equation $3^x = 61.25$ for $x$. 2. **Recall the formula:** To solve for $x$ in an exponential equation $a^x = b$, use logarithms: $x = \log_a b$. 3. **Apply logarithms:** Taking the natural logarithm (ln) on both sides gives: $$\ln(3^x) = \ln(61.25)$$ 4. **Use logarithm power rule:** $$x \ln(3) = \ln(61.25)$$ 5. **Solve for $x$:** $$x = \frac{\ln(61.25)}{\ln(3)}$$ 6. **Calculate values:** $$x \approx \frac{4.114}{1.099} \approx 3.743$$ **Final answer:** $$x \approx 3.743$$