wget -c will resume the download from the point where it stopped (will append to the partially downloaded file). I'm not sure why you're trying to use the wget.log file in this instance.
Code:
user@host$ wget -c 'ftp://slackware.mirrors.tds.net/pub/slackware/slackware-13.37/slackware/xap/mozilla-firefox-4.0-i486-2.txz'
--2011-06-19 11:13:00-- ftp://slackware.mirrors.tds.net/pub/slackware/slackware-13.37/slackware/xap/mozilla-firefox-4.0-i486-2.txz
=> "mozilla-firefox-4.0-i486-2.txz"
Resolving slackware.mirrors.tds.net (slackware.mirrors.tds.net)... 204.246.0.134
Connecting to slackware.mirrors.tds.net (slackware.mirrors.tds.net)|204.246.0.134|:21... connected.
Logging in as anonymous ... Logged in!
==> SYST ... done. ==> PWD ... done.
==> TYPE I ... done. ==> CWD (1) /pub/slackware/slackware-13.37/slackware/xap ... done.
==> SIZE mozilla-firefox-4.0-i486-2.txz ... 11465820
==> PASV ... done. ==> RETR mozilla-firefox-4.0-i486-2.txz ... done.
Length: 11465820 (11M) (unauthoritative)
54% [=============================================> ] 6,304,320 618K/s eta 12s
user@host$ wget -c 'ftp://slackware.mirrors.tds.net/pub/slackware/slackware-13.37/slackware/xap/mozilla-firefox-4.0-i486-2.txz'
--2011-06-19 11:13:27-- ftp://slackware.mirrors.tds.net/pub/slackware/slackware-13.37/slackware/xap/mozilla-firefox-4.0-i486-2.txz
=> "mozilla-firefox-4.0-i486-2.txz"
Resolving slackware.mirrors.tds.net (slackware.mirrors.tds.net)... 204.246.0.134
Connecting to slackware.mirrors.tds.net (slackware.mirrors.tds.net)|204.246.0.134|:21... connected.
Logging in as anonymous ... Logged in!
==> SYST ... done. ==> PWD ... done.
==> TYPE I ... done. ==> CWD (1) /pub/slackware/slackware-13.37/slackware/xap ... done.
==> SIZE mozilla-firefox-4.0-i486-2.txz ... 11465820
==> PASV ... done. ==> REST 6324480 ... done.
==> RETR mozilla-firefox-4.0-i486-2.txz ... done.
Length: 11465820 (11M), 5141340 (4.9M) remaining (unauthoritative)
100%[++++++++++++++++++++++++++++++++++++++++++++++======================================>] 11,465,820 579K/s in 9.7s
2011-06-19 11:13:38 (519 KB/s) - "mozilla-firefox-4.0-i486-2.txz" saved [11465820]