It won't be exactly a log 10 distribution, but rand()**2 * $max would probably be close to what you're looking for.

For example:

$rand_max = 1025;
sub my_rand{
  $rnd = rand;
  return int($rnd*$rnd * $rand_max);
}

@a = ();
for(1..100000) {
  $n = my_rand();
  $a[$n]++;
}

$i = 1;
while($i <= 1024) {
  print "$i: ", $a[$i], $/;
  $i = $i*2;
}
[download]

will produce a distribution similar to this:

1: 1338
2: 913
4: 718
8: 526
16: 397
32: 280
64: 195
128: 137
256: 99
512: 65
1024: 42
[download]

If the curve is too steep (or not steep enough), you can adjust the exponent to 1.5, or 2.5 etc., instead of 2.