Why keep a changelog
Companies and products are increasingly open. Some going as far as publicly displaying their MRR, yet most product or development teams operate in the dark.
Informing users about product updates keeps them engaged and develops trust. Customers can check what your product can and what it can't do yet and that your product is actively being developed.
A changelog will also generate excitement. Many (especially tech-savvy) people prefer products that keep changelogs. Users will be so happy when they see a feature that they have requested in your changelog.
You should keep a changelog, to keep customers informed and excited about product development.
How to keep a good changelog.
How to keep a changelog that keeps customers engaged.