Step 1: Take the natural logarithm of both sides of the inequality. Since the base $1.08 > 1$, the inequality sign remains the same. $$ \ln((1.08)^{n+1}) > \ln(3) $$ Step 2: Use the logarithm property $\ln(a^b) = b \ln(a)$ to bring the exponent down. $$ (n+1) \ln(1.08) > \ln(3) $$ Step 3: Divide both sides by $\ln(1.08)$. Since $1.08 > 1$, $\ln(1.08)$ is positive, so the inequality sign remains the same. $$ n+1 > \frac{\ln(3)}{\ln(1.08)} $$ Step 4: Calculate the numerical values of the logarithms. $$ \ln(3) \approx 1.0986 $$ $$ \ln(1.08) \approx 0.07696 $$ $$ n+1 > \frac{1.0986}{0.07696} $$ $$ n+1 > 14.2749 $$ Step 5: Subtract 1 from both sides to solve for $n$. $$ n > 14.2749 - 1 $$ $$ n > 13.2749 $$ The solution for $n$ is: $$ \boxed{n > 13.2749} $$