I couldn't find the Dropbox log file location but the following workaround maybe useful.
Check your locale by the following command:
$ sudo locale
LANG=en_IN.UTF-8
LANGUAGE=en_IN
LC_CTYPE="en_IN.UTF-8"
LC_NUMERIC="en_IN.UTF-8"
LC_TIME="en_IN.UTF-8"
LC_COLLATE="en_IN.UTF-8"
LC_MONETARY="en_IN.UTF-8"
LC_MESSAGES="en_IN.UTF-8"
LC_PAPER="en_IN.UTF-8"
LC_NAME="en_IN.UTF-8"
LC_ADDRESS="en_IN.UTF-8"
LC_TELEPHONE="en_IN.UTF-8"
LC_MEASUREMENT="en_IN.UTF-8"
LC_IDENTIFICATION="en_IN.UTF-8"
LC_ALL=
Your locale maybe any result other than the above.
As dopbox doesn't work well with some specific locales try to change it to another one preferably en_US.UTF-8 or en_GB.UTF-8
To find available locale on you system try the following command:
$ sudo locale a
And to change the locale use the following command:
$ sudo update-locale LANG=LANG=en_US.UTF-8 LANGUAGE
OR
$ sudo localectl set-locale LANG=en_US.UTF-8
After successful start maybe you could change back to your desired locale.