There are various ways to go about append events to a custom log file in Java.

• Using BufferedOutputStream and FileOutputStream
• Using Log4j (this article)
• Using java.util.logging

Download the latest log4j-core-<version>.jar and log4j-api-<version>.jar files from https://mvnrepository.com and add the JARs to your Java Build Path. 

Create the Log4j.xml file in your project (e.g. WEB-INF/lib/Log4j.xml) and add the following to the Log4j.xml file. In this example, events at log level INFO will be displayed on the console and appended to the app.log file.

<?xml version="1.0" encoding="UTF-8"?> 
<!DOCTYPE xml>
<Configuration> 
  <Appenders> 
    <Console name="LogToConsole" target="SYSTEM_OUT"> 
      <PatternLayout pattern="%d %-5p [%t] %C{2} (%F:%L) - %m%n"/> 
    </Console> 
    <File name="LogToFile" fileName="app.log">
        <PatternLayout>
            <Pattern>%d %p %c{1.} [%t] %m%n</Pattern>
        </PatternLayout>
    </File>    
  </Appenders> 
  <Loggers> 
    <Logger name="default" level="info"/> 
    <Root level="trace"> 
      <AppenderRef ref="LogToFile"/>
      <AppenderRef ref="LogToConsole"/>      
    </Root> 
  </Loggers> 
</Configuration>

Here is an example of how you could log events using Log4j.

import org.apache.logging.log4j.Logger; 
import org.apache.logging.log4j.LogManager;

public class Main {

	private static final Logger logger = LogManager.getLogger(Main.class);
	
	public String hello() {
		String greeting = "Hello World";	
		logger.info(greeting);	
		return greeting;
	}
}