If you want to limit the precision of the log numbers, you can use a format spec in the print statement. %.3f means floating point with 3 decimal places. See below.

#usr/bin/perl -w
use strict;

while(<DATA>)
{
   my($name, @num) = split; 
   print $name; 
   foreach my $num (@num) 
   { 
      printf " %.3f", log10($num); 
   } 
   print "\n"
}

sub log10 
{
   my $n = shift;
   return log($n)/log(10);
}

=prints
name1 3.171 3.157 3.164 3.160 3.021 3.032 3.036 3.022
name2 3.296 3.290 3.239 3.229 3.286 3.302 3.230 3.266
=cut

__DATA__
name1 1481.100 1436.550 1460.410 1444.460 1049.120 1076.890 1085.500 1
+053.100
name2 1978.700 1949.910 1734.030 1694.530 1930.000 2005.530 1696.960 1
+844.810
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