This is the list of actual functions supported by the QGIS field calculator.
If you find something obvious missing, like the log function, please file a feature request ticket in the QGIS bug tracker, example
http://hub.qgis.org/issues/4365
QGIS field calculator functions:
'string' literal string value
number number
NULL null value
sqrt(a) square root
sin(a) sinus of a
cos(a) cosinus of b
tan(a) tangens of a
asin(a) arcussinus of a
acos(a) arcuscosinus of a
atan(a) arcustangens of a
to int(a) convert string a to integer
to real(a) convert string a to real
to string(a) convert number a to string
lower(a) convert string a to lower case
upper(a) convert string a to upper case
length(a) length of string a
atan2(y,x) arcustangens of y/x using the signs of the two arguments to
determine the quadrant of the result.
replace(a,replacethis,withthat) replace replacethis with withthat in string a
regexp_replace(a,replacethis,withthat) replace the regular expression replacethis with withthat in string a
substr(a,from,len) len characters of string a starting from from (first character index is 1)
a || b concatenate strings a and b
$rownum number current row
$area area of polygon
$perimeter perimeter of polygon
$length area of line
$id feature id
$x x coordinate of point
$y y coordinate of point
xat(n) x coordinate of nth point of a line (indizes start at 0; negative
values apply to the last index)
yat(n) y coordinate of nth point of a line (indizes start at 0; negative values apply to the last index)
a ^ b a raised to the power of b
a * b a multiplied by b
a / b a divided by b
a + b a plus b
a - b a minus b
+a positive sign
-a negative value of a