APPLICATION_PATH . "../../data/logs/log.log"
is what ended up working. I always get confused when trying to write these out. Does anyone have any tricks for making it easier to figure out?
APPLICATION_PATH . "../../$config->logfile"
Since /application and /data are on the same level my instinct was to use "../" to leave /application and then go directly into /data. I'm not sure why I am having to use "../../"