MySQL 5.1.73 change default log location
A). To change Mysql innodb_log file to a new location.

 1. Change my.cnf settings for innodb_log file or innodb_fast_shutdown=0 
   (so it does full flush of log files from buffer).

 2. Stop mysql.

 3. Change innodb_log_group_home_dir = /mysql/new_location/ in my.cnf.

 4. Start Mysql, it should be up now. 


B). To change Mysql log_error file to a new location.

 1. Create a new file for log_error file OS level. 
     - copy nul &gt; /mysql/NEW_LOCATION/mysql_error
     - Give mysql permission to /mysql/NEW_LOCATION/mysql_error to read and write.

 2. Change my.cnf log_error = /mysql/NEW_LOCATION/mysql_error 

 3. Stop Mysql.

 4. Start Mysql.


You may do A and B in one shot, I will let you do organize which ever way you wanted.