The log file single write event is associated with writes to the log file header blocks only, and that only happens when a log file is being opened or closed. Header block writes have to be single writes (rather than parallel writes to all the members of the group) because part of the header information is the file number, and that is different for each member. These waits are rare and occur in the background anyway, so I suggest that you not concern yourself with them.

The log file parallel write event is used for routines writes of sets of redo blocks by LGWR. It is interesting only as a point of comparison for the log file sync time, which is what the Ixora 'sync cost ratio' does. Both your calculation of the sync cost ratio, and your interpretation of it are incorrect. Please use the APT script lgwr_stats.sql to calculate the ratio, and check the recent answer on the Log sync cost ratio for some guidelines on how to interpret the number. If you want to know the ratio of background writes to sync writes, then use the redo writes and 'redo synch writes' statistics from V$SYSSTAT instead.

What does the log file single write event mean? What is the difference with log file parallel write event?

In one of my databases I have:

Event                         Average Wait
log file sync                 3.69
log file single write         1.21
log file parallel write       3.80

From this, can I say that my sync cost ratio is 3.69/(1.21 + 3.80) = 0.73. That means that 73% of LGWR writes takes place due to Sync Writes (Commit Statements) and that only 27% of them are due to background writes (log buffer above _log_io_size). Is this correct?