1. **State the problem:** We need to find the value of $n$ in the equation $$2 = 1.05^n$$ where $1.05$ is the base and $2$ is the result after exponentiation. 2. **Recall the formula and rules:** To solve for $n$ in an exponential equation $a^n = b$, we use logarithms: $$n = \log_a b$$ 3. **Apply logarithms:** Taking the natural logarithm (ln) on both sides gives: $$\ln(2) = \ln(1.05^n)$$ 4. **Use logarithm power rule:** $$\ln(2) = n \ln(1.05)$$ 5. **Solve for $n$:** $$n = \frac{\ln(2)}{\ln(1.05)}$$ 6. **Calculate values:** $$\ln(2) \approx 0.6931$$ $$\ln(1.05) \approx 0.04879$$ 7. **Final calculation:** $$n = \frac{0.6931}{0.04879} \approx 14.21$$ **Answer:** The value of $n$ is approximately **14.21**.