Take the natural logarithm of both sides of the inequality.

Since the base $1.08 > 1$, the inequality sign remains the same.

$$\ln((1.08)^{n+1}) > \ln(3)$$

Since $1.08 > 1$, $\ln(1.08)$ is positive, so the inequality sign remains the same.

$$n+1 > \frac{\ln(3)}{\ln(1.08)}$$

$$\ln(3) \approx 1.0986$$ $$\ln(1.08) \approx 0.07696$$ $$n+1 > \frac{1.0986}{0.07696}$$ $$n+1 > 14.2749$$

$$n > 14.2749 - 1$$ $$n > 13.2749$$

The solution for $n$ is: