#!/bin/bash

remoteuser=user_name
remotecomputer=some_ip_address
ssh -l "$remoteuser" "$remotecomputer" "tail -f path/to/log/files/log-`date +"%Y-%m-%d"`.php"

Check in real time changes to a log file. In this case, the file is created by date, one new one per day (a CodeIgniter log file), so some extra items were added to find the log file

Shell script to check log files in real time via ssh

Bash