Here's the `requirements.txt` file for the `blog_app` FastAPI backend with the specified dependencies:

fastapi==0.92.0
uvicorn==0.20.0
sqlalchemy==1.4.46
pydantic==1.10.4
loguru==0.6.0

This `requirements.txt` file includes the following dependencies:

- `fastapi==0.92.0`: The FastAPI web framework.
- `uvicorn==0.20.0`: The ASGI server used to run the FastAPI application.
- `sqlalchemy==1.4.46`: The Python SQL toolkit and Object-Relational Mapping (ORM) library.
- `pydantic==1.10.4`: Data validation and settings management using Python type annotations.
- `loguru==0.6.0`: A library for logging in Python that is intended to be a more user-friendly and efficient alternative to the standard logging module.

Note: The specific versions listed in this `requirements.txt` file may need to be updated to the latest versions based on your project requirements and compatibility with other dependencies.