If eZpublis is set up for several sites you want to have for every site special logfiles.
In site.ini there is a Variable called "LogDir" but this isn't used to store the logfiles under $VarDir/$LogDir

To solve the problem i updated the index.php for our installtion. Hope you can fix this in future releases of eZ publish.
Best Regards
Felix Woldt

>> updated code of index.php

/*!
Reads settings from site.ini and passes them to eZDebug.
*/
function eZUpdateDebugSettings()
{
$ini =& eZINI::instance();

/* New Code from Felix Woldt 31.5.2006
=======================================*/
$deb =& eZDebug::instance();
// The logdir for the actual siteaccess e.g. var/siteaccess/log/
$logDir = $ini->variable( "FileSettings", "VarDir") ."/". $ini->variable( "FileSettings", "LogDir") ."/";

// set the logdir in the Debug object
// a better way is to write a small function in ezdebug.php to do this
$deb->LogFiles = array( EZ_LEVEL_NOTICE => array( $logDir,
"notice.log" ),
EZ_LEVEL_WARNING => array( $logDir,
"warning.log" ),
EZ_LEVEL_ERROR => array( $logDir,
"error.log" ),
EZ_LEVEL_DEBUG => array( $logDir,
"debug.log" ) );

/* New Code - END - from Felix Woldt 31.5.2006
===============================================*/

...
}