A more general way to search for a log is because a particular file will often be located elsewhere depending on the installation and version, as I found that mine is different from previous answers:
/var/log/ is the usual place for application logs.
If it is under restrictive permissions, you can do sudo ls /var/log to get a list of files and directories under it to track your career.
Depending on the version of apache, logs are usually found under the symbol /var/log/apache2 OR /var/log/httpd . Again, if you want to see what specific file you are looking for in this directory, try sudo ls $location$ .
Mine ended up under /var/log/httpd/error_log from my ec2 installation, but error.log is another common file name.
Older error logs and associated access logs are also saved here after they are rotated, with the time stamp when the rotation occurred.
A quick way to view the last 100 or X lines of a file is to use tail -100 /var/log/httpd/error_log .
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