setupLoggingOutputStream.java

private void setupLoggingOutputStream() {
		// get LoggerContext from slf4j
		LoggerContext context = (LoggerContext) LoggerFactory.getILoggerFactory();
		
		// Encoder
		PatternLayoutEncoder encoder = new PatternLayoutEncoder();
		encoder.setContext(context);
		encoder.setPattern("%d{HH:mm:ss} %-5level %logger{36} - %msg%n");
		encoder.start();
		
		OutputStreamAppender<ILoggingEvent> logAppender = new OutputStreamAppender<ILoggingEvent>();
		logAppender.setName("Status zone logging appender");
		logAppender.setContext(context);
		logAppender.setEncoder(encoder);
		logAppender.setOutputStream(new PrintStream(new TextAreaOutputStream(statusZoneCtl.getLogTextArea())));
		logAppender.start();
		
		Logger rootLogger = (Logger) LoggerFactory.getLogger(Logger.ROOT_LOGGER_NAME);
		rootLogger.addAppender(logAppender);
	}

TextAreaOutputStream.java

import java.io.IOException;
import java.io.OutputStream;

import javafx.scene.control.TextArea;

public class TextAreaOutputStream extends OutputStream {
	
	private TextArea textArea;
	
	public TextAreaOutputStream(TextArea ta) {
		textArea = ta;
	}

	@Override
	public void write(int b) throws IOException {
		textArea.appendText(String.valueOf((char)b));
	}

}