You could simply get the character length of the current directory, and remove them from your absolute list
setlocal EnableDelayedExpansion
for /L %%n in (1 1 500) do if "!__cd__:~%%n,1!" neq "" set /a "len=%%n+1"
setlocal DisableDelayedExpansion
for /r . %%g in (*.log) do (
set "absPath=%%g"
setlocal EnableDelayedExpansion
set "relPath=!absPath:~%len%!"
echo(!relPath!
endlocal
)