Which Azure service should be used to create a solution that limits access rates to logic apps?

Using Azure API Management is the most suitable choice for creating a solution that limits access rates to logic apps due to its built-in capabilities for managing and securing APIs. This service allows you to implement rate limiting, which helps control how often clients can call your logic apps, ensuring that they are not overwhelmed by excessive requests. By setting throttling policies, you can define rules about how many requests can be processed in a given timeframe, which is essential for protecting backend services and maintaining performance stability.

Azure Logic Apps, while capable of orchestrating workflows and integrating with various services, does not inherently provide features for direct access rate control. It focuses on automating workflows rather than managing access or traffic.

Azure Functions is designed to execute code in response to events. Although it can be integrated with Logic Apps, it does not offer rate limiting features for managing access to other services.

Azure Event Grid is a service for routing events between source and destination but does not pertain to access management or rate limiting for APIs or workflows.

Thus, Azure API Management stands out as the optimal service for implementing access control measures for logic apps, making it the correct answer for this question.