If it is a single terminal, with only one user using it, no there is no problem.
Bash history can be used as log, but it is only for the user, so it is not safe for security checkups, if you want a more safe log you must configure rsyslog, and consider putting your log in another partition with replication and log rotate.
For example try to log in as some user, do some commands and run kill -9 $$ you will see that logs are not registered in bash history.
To configure rsyslogd the basic you want to do is (in debian for instance):
[CTRL+D for save the file)
And inside (after the first lines)
export PROMPT_COMMAND='RETRN_VAL=$?;logger -p local6.debug "$SSH_CLIENT $(whoami) [$$]: $(history 1 | sed "s/^[ ]*[0-9]\+[ ]*//" ) [$RETRN_VAL]"'