Look at the log file in `/usr/local/var/log/elasticsearch.log`.

**TL;DR**

If you look at the formula definition with:

    brew edit elasticsearch@6

You will find the content of the plist file used for this service, which define the output log as:

    #{var}/log/elasticsearch.log

According to the [documentation](https://www.rubydoc.info/github/Homebrew/brew/Formula:var):

>#var ⇒ Object
>
>The directory where the formula's variable files should be installed. This directory is not inside the HOMEBREW_CELLAR so it persists across upgrades.

According to the [source code](https://github.com/Homebrew/brew/blob/master/Library/Homebrew/formula.rb#L825):

    def var
      HOMEBREW_PREFIX/"var"
    end

You can find the `HOMEBREW_PREFIX` with:

    brew --prefix

It is most likely `/usr/local`. So you will find your log file in `/usr/local/var/log/elasticsearch.log`.