use bugnum;
say log(0.5);
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Hmm .. I suppose you want Math::BigNum and not the unknown bugnum module.

And .. after that, this module does have log functions ..

...

$x->blog();             # logarithm of $x to base e (Euler's number)
$x->blog($base);        # logarithm of $x to base $base (e.g., base 2)
$x->bexp();             # calculate e ** $x where e is Euler's number
$x->bilog2();           # log2($x) rounded down to nearest int
$x->bilog10();          # log10($x) rounded down to nearest int
$x->bclog2();           # log2($x) rounded up to nearest int
$x->bclog10();          # log19($x) rounded up to nearest int
...
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The log functions are called blog.

If I run this ..

tab@music4:~/Pianoforte/Perlmonks 21:54:45 $ cat !$
cat 11156670.pl
#!/usr/bin/perl

use strict;
use warnings;

# use Math::BigNum;

{
    print "Log of .5 is " .  log(0.5) . "\n";
}
tab@music4:~/Pianoforte/Perlmonks 21:54:51 $ ./11156670.pl 
Log of .5 is -0.693147180559945
tab@music4:~/Pianoforte/Perlmonks 21:54:57 $
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.. I get a good value. That presumably uses Perl's built in log function.

I can strongly recommend a complete, self-contained example that shows the output .. this will help you solve things faster.