APM archived log that shows when active box failed over to standby

Failover logs are seen on the ltm log file. Try the below if the log files are not rolled.

egrep -i 'active|standby' /var/log/ltm

egrep -i 'failover|failsafe' /var/log/ltm

egrep -i 'watchdog|overdog' /var/log/ltm

If you think the log files have been rotated, try the below,

zcat /var/log/ltm.*.gz | egrep -i 'active|standby'