1. Given the problem: A piece of land is bought for 3000000 and its price increases at a rate of 3% annually. 2. The question asks: After how many years will the price become 4000000? Round the answer to the nearest year. 3. Let $P_0 = 3000000$ be the initial price, $r = 3\% = 0.03$ the annual growth rate, $P = 4000000$ the future price, and $t$ the number of years. 4. The price grows according to the formula for compound interest: $$ P = P_0 (1 + r)^t $$ 5. Substitute the known values: $$ 4000000 = 3000000 (1 + 0.03)^t $$ 6. Divide both sides by 3000000: $$ \frac{4000000}{3000000} = (1.03)^t $$ $$ \frac{4}{3} = (1.03)^t $$ 7. Take the natural logarithm of both sides: $$ \ln\left( \frac{4}{3} \right) = \ln\left( (1.03)^t \right) $$ 8. Use the logarithm power rule: $$ \ln\left( \frac{4}{3} \right) = t \ln(1.03) $$ 9. Solve for $t$: $$ t = \frac{\ln\left( \frac{4}{3} \right)}{\ln(1.03)} $$ 10. Calculate the values: $$ \ln\left( \frac{4}{3} \right) \approx 0.287682 \quad \text{and} \quad \ln(1.03) \approx 0.029559 $$ $$ t \approx \frac{0.287682}{0.029559} \approx 9.74 $$ 11. Round to the nearest year: $$ t \approx 10 $$ Final answer: It will take approximately 10 years for the price of the land to reach 4000000.