import org.eclipse.core.runtime.ILog;
import org.eclipse.core.runtime.Platform;
// ...
private static final ILog LOGGER = Platform.getLog(NumberHelpers.class);

import java.lang.System.Logger.Level;
// ...
private static final System.Logger LOGGER = System.getLogger(NumberHelpers.class.toString());

import java.lang.System.Logger;

import org.osgi.service.component.annotations.Component;

@Component(service = System.LoggerFinder.class)
public class EclipseLoggerFinder extends System.LoggerFinder {

    @Override
    public Logger getLogger(String name, Module module) {
        return new EclipseLogger(name);
    }

}

import java.lang.System.Logger;
import java.text.MessageFormat;
import java.util.ResourceBundle;

import org.eclipse.core.runtime.ILog;
import org.eclipse.core.runtime.IStatus;
import org.eclipse.core.runtime.Platform;
import org.eclipse.core.runtime.Status;

public class EclipseLogger implements Logger {

    private final String name;

    public EclipseLogger(String name) {
        this.name = name;
    }

    @Override
    public String getName() {
        return name;
    }

    @Override
    public boolean isLoggable(Level level) {
        return level.getSeverity() >= Level.INFO.getSeverity();
    }

    @Override
    public void log(Level level, ResourceBundle bundle, String msg, Throwable thrown) {
        if (isLoggable(level)) {
            try {
                Class<?> cls = Class.forName(name);
                ILog logger = Platform.getLog(cls);
                logger.log(new Status(toIStatus(level), cls, msg, thrown));
            } catch (ClassNotFoundException e) {
                e.printStackTrace();
            }
        }
    }

    @Override
    public void log(Level level, ResourceBundle bundle, String format, Object... params) {
        if (isLoggable(level)) {
            try {
                Class<?> cls = Class.forName(name);
                ILog logger = Platform.getLog(cls);
                logger.log(new Status(toIStatus(level), cls, MessageFormat.format(format, params)));
            } catch (ClassNotFoundException e) {
                e.printStackTrace();
            }
        }
    }

    private int toIStatus(Level level) {
        switch (level) {
        case TRACE:
        case DEBUG:
            return IStatus.OK;
        case INFO:
            return IStatus.INFO;
        case WARNING:
            return IStatus.WARNING;
        case ERROR:
            return IStatus.ERROR;
        default:
            throw new UnsupportedOperationException();
        }
    }

}

<?xml version="1.0" encoding="UTF-8"?>
<scr:component xmlns:scr="http://www.osgi.org/xmlns/scr/v1.1.0" name="com.example.EclipseLoggerFinder">
   <service>
      <provide interface="java.lang.System$LoggerFinder"/>
   </service>
   <implementation class="com.example.EclipseLoggerFinder"/>
</scr:component>

com.example.EclipseLoggerFinder