Redirect Tomcat Embedded 8 Log

Question

I have a web app in Spring Boot that can take a war file and deploy it with embedded tomcat 8. So, for each uploaded war file I do the following

Tomcat tomcat = new Tomcat();
tomcat.setPort(port);
File catalinaHome = new File(TOMCAT_DIR + port);
catalinaHome.mkdirs();
File webapp = new File(TOMCAT_DIR + port + "\\webapps");
webapp.mkdir();
tomcat.setBaseDir(catalinaHome.getAbsolutePath());

try {
    File war = new File("myapp.war");
    StandardContext context = (StandardContext) tomcat.addWebapp("/myapp", war.getAbsolutePath());
    context.setAntiResourceLocking(true);
    tomcat.start();
} catch (Exception e) {
    e.printStackTrace();
}

I don't have any idea how can I redirect the output. I read that tomcat embedded log to System.out, and I was able to redirect to file with:

PrintStream out = new PrintStream(new FileOutputStream("output.txt"));
System.setOut(out);

but redirect all output, and I want something that log to a different file for each tomcat instance that I run. Any solution that I found so far don't resolve my problem. Thanks