Using Log4J 1.*, how can I write two packages to two separate files?

I have the following two packages:

com.mycorp.project.first
com.mycorp.project.second

I'd like to configure Log4J (SLF4J) to write the logs from one package to one file, and from the other package to a second file. I do not want them to be mixed in together.

To be clear, this is one project/one process running.

I've tried filtering and with loggers but they seem to be ignored by log4j. Both files are always identical.

Edit: Thank you for the answers so far, this is what I've got and it's not working. Both output files are identical.

<configuration debug="true">
<contextName>dev</contextName>

<appender name="FIRST_FILE" class="ch.qos.logback.core.rolling.RollingFileAppender">
    <file>A:/dev/LogTesting/logs/first.log</file>
    <filter class="ch.qos.logback.classic.filter.ThresholdFilter">
        <level>INFO</level>
    </filter>
    <rollingPolicy class="ch.qos.logback.core.rolling.TimeBasedRollingPolicy">
        <fileNamePattern>A:/dev/LogTesting/logs/first.%d{yyyyMMdd}%d{_HHmmss,aux}.log.gz</fileNamePattern>
    </rollingPolicy>
    <encoder>
        <pattern>%d{MMM dd HH:mm:ss.SSS} [%thread] %-5level %logger{36} - %msg%n</pattern>
    </encoder>
</appender>

<appender name="SECOND_FILE" class="ch.qos.logback.core.rolling.RollingFileAppender">
    <file>A:/dev/LogTesting/logs/second.log</file>
    <filter class="ch.qos.logback.classic.filter.ThresholdFilter">
        <level>INFO</level>
    </filter>
    <rollingPolicy class="ch.qos.logback.core.rolling.TimeBasedRollingPolicy">
        <fileNamePattern>A:/dev/LogTesting/logs/second.%d{yyyyMMdd}%d{_HHmmss,aux}.log.gz</fileNamePattern>
    </rollingPolicy>
    <encoder>
        <Pattern>%d{MMM dd HH:mm:ss.SSS} %property{HOSTNAME} [%thread] %level %logger{36} %m