You can do that by composing my answer with japhy's:

$l2 = 5;
$h2 = 15;
@data = ( 0.03, 0.1, 0.15, 0.5, 0.7 );

# exponential normalization

$l1 = 0.03;
$h1 = 0.7;
($l1,$h1) = map { 10**$_ } ($l1,$h1);
@normalized =
  map { $l2 + (10**$_ - $l1) * ($h2 - $l2) / ($h1 - $l1) }
  @data;

print " @normalized \n";
# 5 5.47560740136863 5.86545098040508 10.306017857952 15

# logarithmic normalization

$l1 = 0.03;
$h1 = 0.7;
($l1,$h1) = map { log($_) } ($l1,$h1);
@normalized =
  map { $l2 + (log($_) - $l1) * ($h2 - $l2) / ($h1 - $l1) }
  @data;

print " @normalized \n";
# 5 8.82227791363971 10.1095165638026 13.9317944774423 15
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