To use the concept of logistic growth, it is needed to identify the maximum or the limit of population. In this problem, I can't identify what will be the maximum of the population should I use.
The rate of natural increase of the people in a certain city is proportional to the population. If the population increases from $30,000$ to $45,000$ in $10$ years, when will the population be $52,000$?
You have $\frac {dN}{dt}=kN$ . Integrate using limits given in first case and find value of k. Then use this value to find time when population is 52000. For time you have to set appropriate reference.