Where are the PostgreSQL logs on macOS?

The plist used to launch your Postgres on boot may also set the logfile:

$ dir ~/Library/LaunchAgents
org.postgresql.postgres.plist

$ cat ~/Library/LaunchAgents/org.postgresql.postgres.plist
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<dict>
  [...]
  <key>StandardErrorPath</key>
  <string>/usr/local/var/postgres/server.log</string>
</dict>
</plist>

So in this case, /usr/local/var/postgres/server.log.

Just ask your database:

SELECT 
    * 
FROM 
    pg_settings 
WHERE 
    category IN( 'Reporting and Logging / Where to Log' , 'File Locations')
ORDER BY 
    category,
    name;

In my case, it's in "/Library/PostgreSQL/8.4/data/pg_log"

On OSX Homebrew installation the log can be found at:

Latest Homebrew:

/opt/homebrew/var/log/postgres.log

or older:

/usr/local/var/log/postgres.log 

or for older version of postgres (< 9.6)

/usr/local/var/postgres/server.log

Bonus - check if PostgreSQL is running using Homebrew:

brew services info --all