Placeholders and $dbi->quote don't work with table and field names. They only work for data elements.

For identifiers, each database has its own quoting mechanism. The ANSI standard is double quotes:

SELECT foo FROM "$bar"
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SQL Server uses square brackets:

SELECT foo FROM [$bar]
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New versions of DBI have the $dbi->quote_identifier method. It can be used the same as $dbi->quote

my $quoted_log = $dbi->quote_identifier($log)
my $sql = "SELECT foo FROM $quoted_log";
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This may be new enough that DBD::XBase does not support. Then you will have to find out what quoting mechanism it uses and use that.